EX_02/ex_02_apol_1.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In January, a disposable cup industry had a cost of \\$ 27,936.10 for the purchase of raw materials and \\$ 1,243.90 for freight. Using Python, determine what was the total cost for purchasing the raw material?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Total cost was: $29180.00\n"
    }
   ],
   "source": [
    "raw=27936.10\n",
    "freight=1243.90\n",
    "total_cost = raw + freight\n",
    "print('Total cost was: $%.2f' %total_cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Python, find the roots of the function y = 2x^2 + 10x-4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-5.37228132,  0.37228132])"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "source": [
    "import numpy as np \n",
    "c=[2,10,-4]\n",
    "np.roots(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A company's revenue is given by R (x) = 314x and costs by C (x) = 179x + 10530 where x is the marketed quantity of a given product. Determine the respective break-even point using Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "78\n24492\n"
    }
   ],
   "source": [
    "from sympy import *\n",
    "C,R,x=symbols(\"C R x\")\n",
    "init_printing()\n",
    "R=314*x\n",
    "C=179*x+10530\n",
    "xp=solve(Eq(R,C),x)\n",
    "yp=R.subs(x, xp[0])\n",
    "print(xp[0])\n",
    "print(yp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A frozen meat industry conducted a study and concluded that the monthly profit p (x) is given as a function of the price x per kilo of frozen meat and this relationship is described by the polynomial p(x)=-80x+7900x-5000. Determine for which values of x the monthly profit is zero.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([98.11297929,  0.63702071])"
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "source": [
    "import numpy as np \n",
    "c=[-80,7900,-5000]\n",
    "np.roots(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Write the factored form of the expression x^2y^5 + 3x^3y^4-x^3y^6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "  2  4 ⎛   2          ⎞\n-x ⋅y ⋅⎝x⋅y  - 3⋅x - y⎠",
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      "text/latex": "$\\displaystyle - x^{2} y^{4} \\left(x y^{2} - 3 x - y\\right)$"
     },
     "metadata": {},
     "execution_count": 23
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,y = symbols(\"x y\")\n",
    "factor(x**2*y**5+3*x**3*y**4-x**3*y**6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate, using Python, the first derivative of each of the following functions:\n",
    "f(x)=2*x^5+23x^3=7x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "    ⎛         2⎞\n2⋅x⋅⎝69 - 20⋅x ⎠",
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      "text/latex": "$\\displaystyle 2 x \\left(69 - 20 x^{2}\\right)$"
     },
     "metadata": {},
     "execution_count": 30
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,f=symbols(\"x f\")\n",
    "f=-2*x**5+23*x**3-7*x\n",
    "diff(f,x, 2) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the vectors u = (7, 1, -9)\n",
    "and v = (3, -5, -4), calculate u.v and uXv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[[52]]\n[[-49   1 -38]]\n"
    }
   ],
   "source": [
    "import numpy as np \n",
    "u=np.array([[7,1,-9]])\n",
    "v=np.array([[3,-5,-4]])\n",
    "uv=np.inner(u,v)\n",
    "uXv=np.cross(u,v)\n",
    "print(uv)\n",
    "print(uXv)  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obtain the regression line, using python, that best fits these points:\n",
    "A(3,6), B(4,4), C(7,11) and D(10,12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Regression line: y=1.10x+1.65\nCorrelation Coefficient: r=0.90\n"
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as pyp\n",
    "from scipy import stats\n",
    "x=np.array([3,4,7,10])\n",
    "y=np.array([6,4,11,12])\n",
    "a,b,correlation,p,error=stats.linregress(x,y)\n",
    "print('Regression line: y=%.2fx+%.2f'% (a,b))\n",
    "print('Correlation Coefficient: r=%.2f'% correlation)\n",
    "plt.plot(x,y,'o',label='Original data')\n",
    "f=a*x+b\n",
    "plt.plot(x,f,'r',label='Regression Line')\n",
    "plt.ylim(0, 15)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple Interest: We can also calculate the amount, which is the total amount received or due, at the end of the time period. This value is the sum of the interest with initial value (principal).\n",
    "\n",
    "Your formula will be:\n",
    "\n",
    "M = C + J → M = C + C. i. t\n",
    "\n",
    "From the above equation, we therefore have the expression:\n",
    "\n",
    "M = C. (1 + i. t)\n",
    "\n",
    "For interest rate, we can use:\n",
    "\n",
    "M  = C + C.i.t -> M - C = C.i.t -> i = (M-C)/(C.t), then multiply by 100 to have the percentage rate;\n",
    "\n",
    "If the \\$ 1,214.15 invoice was paid 19 days late for a total of \\$ 1,223.11, what is the daily interest rate used?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "The mensal daily is: 0.03884 %\n"
    }
   ],
   "source": [
    "C=1214.15\n",
    "M=1223.11\n",
    "t=19\n",
    "i=(M-C)/(C*t)*100\n",
    "print('The mensal daily is: %.5f %%'%i)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "using python to evolve the equation: (12x^5-3x^4+4x^2)^2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "     10       9      8       7       6       4\n144⋅x   - 72⋅x  + 9⋅x  + 96⋅x  - 24⋅x  + 16⋅x ",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle 144 x^{10} - 72 x^{9} + 9 x^{8} + 96 x^{7} - 24 x^{6} + 16 x^{4}$"
     },
     "metadata": {},
     "execution_count": 96
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,f= symbols(\"x f\")\n",
    "f=(12*x**5-3*x**4+4*x**2)**2\n",
    "expand(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get through python the function that interpolates the points: A(3,6), B(4,4), C(7,11) and D(10,12):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "3         2\n-0.2024 x + 3.917 x - 21.93 x + 42\n"
    }
   ],
   "source": [
    "from scipy.interpolate import *\n",
    "x=[3,4,7,10]\n",
    "y=[6,4,11,12]\n",
    "f=lagrange(x,y)\n",
    "\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve, using python, the linear programming problem:\n",
    "\n",
    "Maxz = 3*x1 + 4*x2 + 2*x3\n",
    "\n",
    "1*x1+10*x2+4*x3 <= 120\n",
    "\n",
    "4*x1+1*x2 <= 80\n",
    "\n",
    "2*x2+3*x3 <= 78\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Product_A = 20.0\nProduct_B = 0.0\nProduct_C = 25.0\nMax Profit =  110.0\n"
    }
   ],
   "source": [
    "from pulp import *\n",
    "prob=LpProblem('Example', LpMaximize)\n",
    "x1=LpVariable(\"Product A\", 0)\n",
    "x2=LpVariable(\"Product B\", 0)\n",
    "x3=LpVariable(\"Product C\", 0)\n",
    "prob += 3*x1 + 4*x2 + 2*x3\n",
    "prob += 1*x1+10*x2+4*x3 <= 120\n",
    "prob += 4*x1+1*x2 <= 80\n",
    "prob += 2*x2+3*x3 <= 78\n",
    "prob.solve()\n",
    "for v in prob.variables():\n",
    "    print(v.name,\"=\", v.varValue)\n",
    "print(\"Max Profit = \", value(prob.objective))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the expression that relates the cost c referring to the daily production of x units in an industry is motorcycles is given by the function\n",
    "c (x) = 2x^2+7x+9000; get the cost for 30 units:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "11010",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle 11010$"
     },
     "metadata": {},
     "execution_count": 109
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,y=symbols(\"x y\")\n",
    "y=2*x**2+7*x+9000\n",
    "y.subs(x,30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A car costs cash $64,700.00, but will be paid in 8 equal installments without interest; What is the value of each installment?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "8087.5\n"
    }
   ],
   "source": [
    "c=64700\n",
    "t=8\n",
    "bill=c/t\n",
    "print(bill)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A resistor has a voltage y as a function of the current x described by the equation f(x)=x^2+8x, make the graph to illustrate the behavior of the resistor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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nJSbqOnORaPH8J1u475XPGdgxgZfuGKAQqaTOGCRmdiOwGLgBuBFYZGbXl2Kf6UC6uy8Kll8lEiwZZtYi2GcLILPY+m2Kbd8a2Bm0tz5Ju4hEOXfnT++t51f/t4Yh3c9h8m39qBen294qq5IMtv8c6Ofuo919FNAf+O+z3aG77wbSzKxL0HQ5sAaYC4wO2kYDbwTv5wIjzCzOzDoQGVRfHJwGyzazgWZmwKhi24hIlCoscn7++ir+siCV4UlteOrm3sTVqH7mDSU0JYn4au6eWWx5L6V/1vuPgOlmVgvYDNwefOcsMxsLbCdyBIS7rzazWUTCpgAY7+7H72e5m/9c/vs2GmgXiWq5BYX89OXPeXPlLu6+7Fzuv6oLkX8nSmVWkiB5x8zeBWYEy8OJ3LNx1tx9OZH7U050+SnWfwR45CTtyUTuRRGRKJedk8/3X0zh0017eejqrtxxScewS5ISOmOQuPv/M7PrgMFEBrgnuftr5V6ZiFQZmdk53DZ5CRsysnl8eE+G9dYDqaJJiUav3H02MLucaxGRKmjrniOMmryYPYdzeXZ0Epd1aXbmjaRSOWWQmNnH7n6xmWXzxctqDXB3jy/36kQkpi1PO8CYKUsAeOnOgfRq0yjcguSsnDJI3P3i4FXzEIhImVuwLoPx05eR2CCOqWP606FpvbBLkrNUkvtIzjWzuOD9ZWZ2TzDpoojIWXl5yXbufCGFc5vVY/bdgxQiUa4kl/HOBgrNrBPwHNABeKlcqxKRmOTuPPbeeh6YvZLBnZoyc9xFJDaIC7ssKaWSDLYXuXuBmQ0DnnD3v5jZsvIuTERiS15BERPmrGT20nSGJ7Xh4WE9qFm9tLekSWVQkiDJN7ObiNxtfk3QVrP8ShKRWHMoJ5+7p6XwSepefnLFedxzeSfdaBhDShIktwN3AY+4+5ZgmpJp5VuWiMSKHQeOcfvzi9mcdYQ/3tCT6/vqHpFYU5IbEtcA9xRb3gL8rjyLEpHYsGrHQcZMWcKx/EKmjunP4E5Nwy5JykFJntk+mMgzSdoF6x+/j0TzF4jIKc1bk8E9M5aRUK8W0+4YwHnNdSdBrCrJqa3ngJ8QeQBV4RnWFZEqzt2Z/MlWHn5zDRe2asgzo5No1kBPNIxlJQmSg+6uWXVF5IzyC4v41f+tZtrC7Qzpfg6PD+9FnVqaAj7WlSRIPjCzPwBz+OIz25eWW1UiEnUOHsvnhy8t5aONe/j+1zrywJDzqVZNV2ZVBSUJkgHBa/Fp3x34RtmXIyLRaPveo4yZuoSte47w++su5MZ+bc68kcSMkly19fWKKEREotNnm/byg+kpOPDi2AFcdG6TsEuSClaSubaam9lzZvZ2sNwteIqhiFRxMxZv59bnFpFQrxav/2CwQqSKKsn8BFOAd4GWwfIG4MflVI+IRIGCwiJ+OXc1E+asZFCnpsz5wWDaa+LFKuuUQWJmx097NXX3WUARgLsXoMuARaqsA0fzuO35JUz5dCu3D27P5NFJNKyjWZOqstONkSwG+gBHzKwJwcOtzGwgcLACahORSiY1M5s7piaz48AxDarLv50uSI5ft/dTYC5wrpl9AiQC15d3YSJSucxbk8FPXl5O7ZrVmHHnQJLaJ4RdklQSpwuSRDP7afD+NeAtIuGSC1wBrCjn2kSkEigqcp76IJXH5m3gglYN+futfWnZqE7YZUklcrogqQ7U5z9HJsfVLb9yRKQyOZxbwM9mfc47q3czrHcrfvu9C6hdU3eqyxedLkh2ufv/VlglIlKpbMo6zPdfTGFz1mEeurorYy/uoGeIyEmVZIxERKqY94PxkJo1qjFt7AAGafp3OY3TBcnlFVaFiFQKhUXOk+9v4M8LUunRKp6nR/aldWOdzZbTO2WQuPu+iixERMJ14Gge985czocbsrihb2t+PbSHxkOkREoyaaOIxLiV6Qe5e3oKmYdy+c2wC7ipfxuNh0iJlWSKlHJhZtXNbJmZ/SNYTjCzeWa2MXhtXGzdCWaWambrzeyqYu19zWxl8NmfTX/yRb4Sd+elRdu5buKnFBU5s+66iJsHtFWIyFcSWpAA9wJriy0/CMx3987A/GAZM+sGjAC6A0OAv5nZ8ePticA4oHPwM6RiSheJfkfzCrjvlc/5r9dWMqBjAv+45xJ6tWkUdlkShUIJEjNrDVwNPFus+VpgavB+KjC0WPtMd8919y1AKtDfzFoA8e7+mbs78EKxbUTkNFIzDzP0r5/w2rId3Ht5Z6bc3p+EerXCLkuiVFhjJE8A9wMNirU1d/ddAO6+y8yaBe2tgIXF1ksP2vKD9ye2f4mZjSNy5ELbtm3LoHyR6PXG8h1MmLOS2jWrM/X2/nztvMSwS5IoV+FHJGb2HSDT3VNKuslJ2vw07V9udJ/k7knunpSYqL80UjXl5BcyYc5K7p25nG4t4nnrnksUIlImwjgiGQx818y+DdQG4s1sGpBhZi2Co5EWQGawfjpQfIrR1sDOoL31SdpF5ASbsg4zfvpS1u3O5vuXduRn3+xCzephDpFKLKnwP0nuPsHdW7t7eyKD6AvcfSSRGYZHB6uNBt4I3s8FRphZnJl1IDKovjg4DZZtZgODq7VGFdtGRAJzlqZzzV8+JuNQDs/f1o8J3+qqEJEyVZnuI/kdMCt4jO924AYAd19tZrOANUABMN7djz9Y624iT3CsA7wd/IgIcCS3gP9+YxVzlu6gf4cEnhzRixYNNWuvlD2LXPBUdSQlJXlycnLYZYiUq1U7DnLPjGVs3XuEey7vzI++0Znq1XRviJw9M0tx96STfVaZjkhEpJSKipzJn2zh0XfW0aReHC/dOZCBHZuEXZbEOAWJSIzIys7lvlc+518bsriyW3N+f92FNNa9IVIBFCQiMWD+2gzuf3UFh3ML+PXQHozUNCdSgRQkIlHsWF4hj7y1hmkLt9O1RTwzR/Sic/MGZ95QpAwpSESi1Ir0A/z45eVszjrCnZd04GdXdSGuhqZ9l4qnIBGJMgWFRUz85yaenL+RxAZxTL9jAIP1BEMJkYJEJIps2XOEn85azrLtB/huz5b8+toeNKxbM+yypIpTkIhEgaIiZ9qibfz2rXXUqlGNJ0f04tpeJ52jVKTCKUhEKrkdB47xwKsr+Dh1D5eel8jvr7+Q5vG1wy5L5N8UJCKVlLszKzmNX/9jLUXuPDKsBzf312W9UvkoSEQqoZ0HjjFhzko+3JDFwI4J/OH6nrRJqBt2WSInpSARqUTcnZeXpPHIm2spKHJ+cU03Rl/UnmqaJ0sqMQWJSCWRtu8oE+as5OPUPVzUsQmPXnchbZvoKEQqPwWJSMgKi5ypn27lD++up3o14+GhkbEQHYVItFCQiIRo/e5sHpyzgmXbD3BZl0R+M+wCWjbSM0MkuihIREKQk1/I3z5IZeKHm6gfV4PHh/dkaK9WuiJLopKCRKSCLdy8l/96bSWbs44wrHcrHrq6K03qx4VdlshZU5CIVJB9R/L4zVtreTUlnTYJdZg6pj+XnpcYdlkipaYgESlnRUXOqynp/PbttWTnFHD3Zedyzzc6U6eWZuqV2KAgESlH63dn8/PXVpK8bT9J7Rrz8LAenH9OfNhliZQpBYlIOcjOyefJ9zfy/Kdbia9dg99fdyHX922tS3olJilIRMqQuzP385088uZasg7nMqJfG/7fVeeToGenSwxTkIiUkTU7D/HLuatZvHUfF7ZuyKRRSfRq0yjsskTKnYJEpJT2H8njsXkbmL5oGw3r1OQ3wy5geL82VNdpLKkiFCQiZym/sIjpC7fx+Psbyc7J59aB7fjplV30xEKpchQkImfhww1ZPPyPNWzMPMzgTk347+9009VYUmUpSES+go0Z2Tz85lo+3JBFuyZ1mXRrX67s1lxTm0iVVuFBYmZtgBeAc4AiYJK7P2lmCcDLQHtgK3Cju+8PtpkAjAUKgXvc/d2gvS8wBagDvAXc6+5ekf2RqiErO5cn3t/AzCVp1K1VnYeu7sqtF7UjroZuKhQJ44ikALjP3ZeaWQMgxczmAbcB8939d2b2IPAg8ICZdQNGAN2BlsD7ZnaeuxcCE4FxwEIiQTIEeLvCeyQx62heAc9+tIW/f7iJ3IIiRg5oy71XnKfLeUWKqfAgcfddwK7gfbaZrQVaAdcClwWrTQX+CTwQtM9091xgi5mlAv3NbCsQ7+6fAZjZC8BQFCRSBgoKi3g5OY0n3t9IVnYuQ7qfw/1DutAxsX7YpYlUOqGOkZhZe6A3sAhoHoQM7r7LzJoFq7UicsRxXHrQlh+8P7H9ZPsZR+TIhbZt25ZhDyTWuDvvrNrNH95bz+asIyS1a8zEW/qQ1D4h7NJEKq3QgsTM6gOzgR+7+6HTDFae7AM/TfuXG90nAZMAkpKSNIYiX+LufJy6hz+8u54V6Qfp1Kw+z4xK4oquzTSQLnIGoQSJmdUkEiLT3X1O0JxhZi2Co5EWQGbQng60KbZ5a2Bn0N76JO0iX8mSrfv403vrWbh5H60a1eGPN/RkWO9WuqFQpITCuGrLgOeAte7+WLGP5gKjgd8Fr28Ua3/JzB4jMtjeGVjs7oVmlm1mA4mcGhsF/KWCuiEx4PO0Azw2bwMfbsiiaf04fnFNN24e0FZXYol8RWEckQwGbgVWmtnyoO2/iATILDMbC2wHbgBw99VmNgtYQ+SKr/HBFVsAd/Ofy3/fRgPtUgIr0w/yxPsbmL8uk0Z1azLhW+cz6qL2ej6IyFmyqnbbRVJSkicnJ4ddhoRgRfoB/jw/lffXZtCwTk3uvKQDowe1p0FtTWkiciZmluLuSSf7THe2S8xbun0/f5m/kQ/WZ9GwTk1+euV53Da4PfEKEJEyoSCRmOTufLppL08tSOWzzXtJqFeL+4d04daB7XQEIlLGFCQSU4qKnPfWZDDxw018nnaAZg3ieOjqrtzUvy314vTHXaQ86G+WxITcgkLeWLaTp/+1ic1ZR2iTUIeHh/bg+r6tqV1Tg+gi5UlBIlHt4NF8pi3axpRPt5KVnUu3FvH8+abefLvHOdSoXi3s8kSqBAWJRKVte4/w/CdbmZWcxtG8Qi7p3JTHbuzJxZ2a6k50kQqmIJGo4e58tnkvUz7Zyry1GdSoZlzTsyV3XNyRbi31UCmRsChIpNI7llfIG8t3MOXTrazbnU1CvVr88OuduHVgO5rF1w67PJEqT0EildbWPUeYtnAbs5LTOJRTQNcW8fz++gv5bs+WGkAXqUQUJFKpFBQW8f7aTKYv2sZHG/dQo5oxpMc5jLqoPf3aN9b4h0glpCCRSiFt31FmJacxKzmNjEO5tGhYmx9f0Zmb+7fV6SuRSk5BIqHJyS9k3poMZiWn8XHqHgy49LxEHhnajsu6JOryXZEooSCRCuXurNpxiFdT0nh9+U4OHsunZcPa3Ht5Z25MakPLRnXCLlFEviIFiVSIjEM5vL5sB7OXprMh4zC1alTjqu7ncGNSawad21QPkRKJYgoSKTfZOfm8s2o3ry/fwaeb9uIOvds24uGhPbjmwpY0rKvJE0VigYJEytSxvEIWrMtk7uc7+GB9FnkFRbRrUpcffaMzQ3u1pGNi/bBLFJEypiCRUjuWV8g/12fyj5W7WLA2k2P5hSQ2iOOWAW25pmdLerdppMt2RWKYgkTOSnZOPgvWZfLOqt38c30Wx/ILaVKvFsP6tOI7F7RgQMcmGvcQqSIUJFJiuw4e4/01Gby3JoOFm/eSX+gkNojjur6t+FaPFgzokKBLdkWqIAWJnFJhkbMi/QAL1mUyf20ma3YdAqBD03rcPrgD3+zWnD5tG1NNRx4iVZqCRL4gMzuHjzfu4cMNWfxrQxb7j+ZTzSCpXQIPfut8rujajHMT62vMQ0T+TUFSxR3NK2DJ1v18mrqHf23cw9rgqKNJvVp8vUszLu2SyKXnJdKobq2QKxWRykpBUsUcyytk6fb9LNq8l4Wb97EsbT/5hU7N6kZSuwTuH9KFSzol0r1lvE5ZiUiJKEhi3P4jeaRs28+SbftYsmUfK3ccJL/QqWbQo1VDxl7ckUHnNqFf+wTq1NLU7CLy1SlIYkh+YRHrd2ezPO0Ay9MOsHTbfjbvOQJAzerGBa0aMmZwBwZ2bEJS+8Y0qK07y0Wk9BQkUSqvoIjUzMOs2nmQVTsOsiL9IGt3HSK3oAiAhHq16NO2MdcntaZP28b0atNID4MSkXKhIKnk3J2MQ7msz8hm/e5DrNudzbpd2WzMzCa/0AGoH1eDbi3juXVgO3q2aUSvNo1o3biOrqwSkQqhIKkkcvIL2b7vKJuzjrB5z2G2ZB0hNeswqRmHyc4t+Pd6zRrE0eWcBnztvI50axlP95bxdGhSTwPjIhKaqA8SMxsCPAlUB55199+FXNJJ5eQXsutgDrsOHGPnwRzS9h0lff8x0vYfZfveo+w+lPOF9Zs1iKNjYj2G9WlF52b16dSsAeef04DG9XQZrohULlEdJGZWHfgrcCWQDiwxs7nuvqa8951fWMShY/kcDH72H81j35F89h/JY8/hXLIO55KVnUvmoVwysnM4cDT/hNrhnPjatGpUh0GdmtC+ST3aNalLh6b16NC0ngbCRSRqRHWQAP2BVHffDGBmM4FrgTIPkpeXbOfvH24mO7eAwzkFHMsvPOW6tWpUI7F+HE3r16Jtk7r075BAswZxtGxUhxaNatOyYeQ1roYGv0Uk+kV7kLQC0ootpwMDTlzJzMYB4wDatm17VjtKqBdHt5bxNKhdg/pxNagfV5OGdWrQsG5NGtapSUK9OBLq1qJRvZo0iKuhgW4RqTKiPUhO9tvav9TgPgmYBJCUlPSlz0viym7NubJb87PZVEQkpkX7nN/pQJtiy62BnSHVIiJSJUV7kCwBOptZBzOrBYwA5oZck4hIlRLVp7bcvcDMfgi8S+Ty38nuvjrkskREqpSoDhIAd38LeCvsOkREqqpoP7UlIiIhU5CIiEipKEhERKRUFCQiIlIq5n5W9+dFLTPLArad5eZNgT1lWE40UJ+rBvW5aihNn9u5e+LJPqhyQVIaZpbs7klh11GR1OeqQX2uGsqrzzq1JSIipaIgERGRUlGQfDWTwi4gBOpz1aA+Vw3l0meNkYiISKnoiEREREpFQSIiIqWiICkhMxtiZuvNLNXMHgy7nvJgZm3M7AMzW2tmq83s3qA9wczmmdnG4LVx2LWWJTOrbmbLzOwfwXKs97eRmb1qZuuC/9cXVYE+/yT4M73KzGaYWe1Y67OZTTazTDNbVaztlH00swnB77P1ZnZVafatICkBM6sO/BX4FtANuMnMuoVbVbkoAO5z967AQGB80M8Hgfnu3hmYHyzHknuBtcWWY72/TwLvuPv5QE8ifY/ZPptZK+AeIMndexB55MQIYq/PU4AhJ7SdtI/B3+sRQPdgm78Fv+fOioKkZPoDqe6+2d3zgJnAtSHXVObcfZe7Lw3eZxP5BdOKSF+nBqtNBYaGUmA5MLPWwNXAs8WaY7m/8cDXgOcA3D3P3Q8Qw30O1ADqmFkNoC6RJ6nGVJ/d/V/AvhOaT9XHa4GZ7p7r7luAVCK/586KgqRkWgFpxZbTg7aYZWbtgd7AIqC5u++CSNgAzUIsraw9AdwPFBVri+X+dgSygOeD03nPmlk9YrjP7r4D+COwHdgFHHT394jhPhdzqj6W6e80BUnJ2EnaYva6aTOrD8wGfuzuh8Kup7yY2XeATHdPCbuWClQD6ANMdPfewBGi/5TOaQXjAtcCHYCWQD0zGxluVaEr099pCpKSSQfaFFtuTeTQOOaYWU0iITLd3ecEzRlm1iL4vAWQGVZ9ZWww8F0z20rkdOU3zGwasdtfiPxZTnf3RcHyq0SCJZb7fAWwxd2z3D0fmAMMIrb7fNyp+limv9MUJCWzBOhsZh3MrBaRQaq5IddU5szMiJw7X+vujxX7aC4wOng/GnijomsrD+4+wd1bu3t7Iv9PF7j7SGK0vwDuvhtIM7MuQdPlwBpiuM9ETmkNNLO6wZ/xy4mM/8Vyn487VR/nAiPMLM7MOgCdgcVnuxPd2V5CZvZtIufTqwOT3f2RcCsqe2Z2MfARsJL/jBn8F5FxkllAWyJ/KW9w9xMH9aKamV0G/Mzdv2NmTYjh/ppZLyIXF9QCNgO3E/lHZSz3+VfAcCJXJi4D7gDqE0N9NrMZwGVEporPAH4BvM4p+mhmPwfGEPlv8mN3f/us960gERGR0tCpLRERKRUFiYiIlIqCRERESkVBIiIipaIgERGRUlGQiJQBMzvHzGaa2SYzW2Nmb5nZeRW4/8vMbFBF7U+kOAWJSCkFN7m9BvzT3c91925E7r9pXsLtq59uuYQuI3K3tkiFU5CIlN7XgXx3f/p4g7svB6off8YJgJk9ZWa3Be+3mtn/mNnHwA0nWf6mmX1mZkvN7JVg/rPj2/0qaF9pZucHE2zeBfzEzJab2SUV1nMRFCQiZaEHcDYTP+a4+8XuPrP4MvA+8BBwhbv3AZKBnxbbbk/QPpHI3fhbgaeBx929l7t/dLYdETkbNcIuQKQKe/kUywOJPEDtk8hZM2oBnxVb7/hkminA98qzQJGSUJCIlN5q4PqTtBfwxaP+2id8fuQUywbMc/ebTrG/3OC1EP0dlkpAp7ZESm8BEGdmdx5vMLN+RCb47BbMsNqQyKyzJbEQGGxmnYLvqluCK8CygQZfvXSR0lOQiJSSR2Y+HQZcGVz+uxr4JZHnO8wCVgDTicw6W5LvywJuA2aY2QoiwXL+GTb7P2CYBtslDJr9V0RESkVHJCIiUioKEhERKRUFiYiIlIqCRERESkVBIiIipaIgERGRUlGQiIhIqfx/L543SWiwhfkAAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt \n",
    "import numpy as np \n",
    "x=np.linspace(0, 100, 100)\n",
    "y=x**2+8*x\n",
    "plt.plot(x,y)\n",
    "plt.xlabel('Current')\n",
    "plt.ylabel('Tension')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the vectors u = (3, -2, 1) and v = (6, 5, -7), calculate u.v:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[[1]]\n"
    }
   ],
   "source": [
    "import numpy as np \n",
    "u=np.array([[3,-2,1]])\n",
    "v=np.array([[6,5,-7]])\n",
    "uv=np.inner(u,v)\n",
    "uXv=np.cross(u,v)\n",
    "print(uv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cost c for the daily production of x units of a certain product corresponds to c(x)=2x^2-40x+1000; What is the level of production that minimizes the cost?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([10.+20.j, 10.-20.j])"
     },
     "metadata": {},
     "execution_count": 120
    }
   ],
   "source": [
    "import numpy as np \n",
    "c=[2,-40,1000]\n",
    "np.roots(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the definite integral of the function f(x)=x^3+cos(x) in the range \\[0,2\\]: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "sin(2) + 4",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle \\sin{\\left(2 \\right)} + 4$"
     },
     "metadata": {},
     "execution_count": 123
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,f=symbols(\"x f\")\n",
    "init_printing()\n",
    "f=x**3+cos(x)\n",
    "integrate(f,(x,0,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using python, solve the following linear system:\n",
    "\n",
    "4x-3y+z=15\n",
    "\n",
    "x+y+3z=27\n",
    "\n",
    "2x+3y-4z=31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[[9.2345679 ]\n [8.35802469]\n [3.13580247]]\n"
    }
   ],
   "source": [
    "import numpy as np\n",
    "A=np.array([[4,-3,1],[1,1,3],[2,3,-4]])\n",
    "b=np.array([[15],[27],[31]])\n",
    "x=np.linalg.solve(A, b)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Python, find the roots of the function f(x)=-2x^3+7x^2-20x+6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([1.58217509+2.53665299j, 1.58217509-2.53665299j,\n       0.33564982+0.j        ])"
     },
     "metadata": {},
     "execution_count": 131
    }
   ],
   "source": [
    "import numpy as np \n",
    "c=[-2,7,-20,6]\n",
    "np.roots(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a soccer match, an unusual move occurred: the goalkeeper, when shooting the goal, hit the ball inside the opponent's goal, the trajectory described by the ball was a parabola calculated by the f(x)=-0.008x^2+0.8x equation; determine the total distance between the point where the ball was kicked and the point where it touches the ground."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([100.,   0.])"
     },
     "metadata": {},
     "execution_count": 132
    }
   ],
   "source": [
    "import numpy as np \n",
    "c=[-0.008,0.8,0]\n",
    "np.roots(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the vectors u = (3, -2, 1) and v = (6, 5, -7), calculate u.v and uXv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[[1]]\n[[ 9 27 27]]\n"
    }
   ],
   "source": [
    "import numpy as np \n",
    "u=np.array([[3,-2,1]])\n",
    "v=np.array([[6,5,-7]])\n",
    "uv=np.inner(u,v)\n",
    "uXv=np.cross(u,v)\n",
    "print(uv)\n",
    "print(uXv)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the indefinite integral of the function:\n",
    "\n",
    "f’(x) = x³+cos(x);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": " 4         \nx          \n── + sin(x)\n4          ",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle \\frac{x^{4}}{4} + \\sin{\\left(x \\right)}$"
     },
     "metadata": {},
     "execution_count": 135
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,f=symbols(\"x f\")\n",
    "init_printing()\n",
    "f=x**3+cos(x)\n",
    "integrate(f,x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "A company not opting for the simple Brazilian national (Super Simples), pays 68.18% of tax on the salary of each monthly employee and the total monthly cost referring to the wages plus tax of 12 employees, who receive the same salary, corresponds to $ 137,236.64. so what is the free salary for each of these employees?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "The salary of each employees is: $ 6800.09\n"
    }
   ],
   "source": [
    "salaries=137236.64\n",
    "tax=1.6818\n",
    "employees=12\n",
    "salary=(salaries)/(tax*employees)\n",
    "print('The salary of each employees is: $ %.2f' %salary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the second derivative of the function: f(x)=19x^6-33x^3+111x+19?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "       4        \n- 570⋅x  - 198⋅x",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle - 570 x^{4} - 198 x$"
     },
     "metadata": {},
     "execution_count": 148
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,f=symbols(\"x f\")\n",
    "f=-19*x**6-33*x**3+111*x+19\n",
    "expand(diff(f,x, 2)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let the function be f(x)=-4x2^+40x-7; Obtain the area between the graph of f delimited by the x axis Make the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Area= -4*x**3/3 + 20*x**2 - 7*x\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt \n",
    "import numpy as np \n",
    "import sympy as sy\n",
    "x,f=symbols(\"x f\")\n",
    "f=-4*x**2+40*x-7\n",
    "A=integrate(f,(x))\n",
    "x=np.linspace(-1,3,1000)\n",
    "f=-4*x**2+40*x-7\n",
    "plt.plot(x,f, color='blue')\n",
    "plt.axhline(color='blue')\n",
    "plt.fill_between(x,f, where=[(x>0.2)and(x<2)for x in x], color='green')\n",
    "print('Area=', A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the polynomials that interpolate the points: A(0,2), B(3,7) and C(10,-2):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "2\n-0.2952 x + 2.552 x + 2\n"
    }
   ],
   "source": [
    "from scipy.interpolate import *\n",
    "x=[0,3,10]\n",
    "y=[2,7,-2]\n",
    "f=lagrange(x,y)\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which is the line that interpolates the points: A(2,5) and B(7,10)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "\n1 x + 3\n"
    }
   ],
   "source": [
    "from scipy.interpolate import *\n",
    "x=[2,7]\n",
    "y=[5,10]\n",
    "f=lagrange(x,y)\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a bicycle factory, production in the third month of a certain year was 2,000 units and production in the sixth month was 3,000 units; which is the line that interpolates these points (in thousands) ?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "\n0.3333 x + 1\n"
    }
   ],
   "source": [
    "from scipy.interpolate import *\n",
    "x=[3,6]\n",
    "y=[2000,3000]\n",
    "f=lagrange(x,y)\n",
    "print(f/1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the definite integral of the function f(x)=5x^2+3x+1 in the range x=0 and x=4.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "404/3",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle \\frac{404}{3}$"
     },
     "metadata": {},
     "execution_count": 167
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,f=symbols(\"x f\")\n",
    "init_printing()\n",
    "f=5*x**2+3*x+1\n",
    "integrate(f,(x,0,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following table represents the sale of hospital equipment:\n",
    "\n",
    "1-180\n",
    "\n",
    "2-120\n",
    "\n",
    "3-150\n",
    "\n",
    "4-190\n",
    "\n",
    "5-210\n",
    "\n",
    "which line best fits these points?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Regression line: y=13.00x+131.00\nCorrelation Coefficient: r=0.58\n"
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as pyp\n",
    "from scipy import stats\n",
    "x=np.array([1,2,3,4,5])\n",
    "y=np.array([180,120,150,190,210])\n",
    "a,b,correlation,p,error=stats.linregress(x,y)\n",
    "print('Regression line: y=%.2fx+%.2f'% (a,b))\n",
    "print('Correlation Coefficient: r=%.2f'% correlation)\n",
    "plt.plot(x,y,'o',label='Original data')\n",
    "f=a*x+b\n",
    "plt.plot(x,f,'r',label='Regression Line')\n",
    "plt.ylim(140, 200)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate, using Python, the first derivative of each of the following functions: f(x)=18*x^4-14x^2+22*X-1.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "      3            \n- 72⋅x  - 28⋅x + 22",
      "image/png": "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\n",
      "text/latex": "$\\displaystyle - 72 x^{3} - 28 x + 22$"
     },
     "metadata": {},
     "execution_count": 173
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,f=symbols(\"x f\")\n",
    "f=-18*x**4-14*x**2+22*x-1\n",
    "diff(f,x) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a bicycle factory, production in the third month of a certain year was 2,000 units and production in the sixth month was 3,000 units; What is the forecast for the seventh month?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "\n0.3333 x + 1\n"
    }
   ],
   "source": [
    "from scipy.interpolate import *\n",
    "x=[3,6]\n",
    "y=[2000,3000]\n",
    "f=lagrange(x,y)\n",
    "print(f/1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A manager wants to find the relationship between the number of hours that a plant is operational in a week and weekly production.\n",
    "Here the independent variable x is hours of operation, and the dependent variable y is production volume.\n",
    "The manager develops the following table:\n",
    "\n",
    "x -  y\n",
    "\n",
    "34 - 102\n",
    "\n",
    "35 - 104\n",
    "\n",
    "39 - 137\n",
    "\n",
    "42 - 148\n",
    "\n",
    "43 - 150\n",
    "\n",
    "47 - 158\n",
    "\n",
    "production Hour (x) - Production Volume (y)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "y=-46.0 + 4.5\n"
    }
   ],
   "source": [
    "from scipy.stats import linregress\n",
    "x=[34,35,39,42,43,47]\n",
    "y=[102,109,137,148,150,158]\n",
    "slope=round(linregress(x,y).slope,1)\n",
    "intercept=round(linregress(x,y).intercept,1)\n",
    "print(f'y={intercept} + {slope}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Regression line: y=4.50x+-46.00\nCorrelation Coefficient: r=0.97\n"
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "x=np.array([34,35,39,42,43,47])\n",
    "y=np.array([102,109,137,148,150,158])\n",
    "a,b,correlation,p,error=stats.linregress(x,y)\n",
    "print('Regression line: y=%.2fx+%.2f'% (a,b))\n",
    "print('Correlation Coefficient: r=%.2f'% correlation)\n",
    "plt.plot(x,y,'o',label='Original data')\n",
    "f=a*x+b\n",
    "plt.plot(x,f,'r',label='Regression Line')\n",
    "plt.ylim(100, 180)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you want to buy some tapes and CDs. Does anyone really buy tapes anymore? Anyway, you can buy up to 11 tapes; You can buy up to 7 CDS, but you want at least 3; You must get enough tapes or CDs to hold at least 10 hours of music; Each tape holds about 45 minutes of music and each CD holds an hour a tape costs $8 and a CD costs $12; So how many tapes and CDs should you buy to minimize your cost?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "CD = 7.0\nTape = 4.0\nTotal Cost =  116.0\n"
    }
   ],
   "source": [
    "from pulp import *\n",
    "prob=LpProblem('Example', LpMaximize)\n",
    "x1=LpVariable(\"Tape\", 0)\n",
    "x2=LpVariable(\"CD\", 0)\n",
    "prob += x1<=11\n",
    "prob += x2>=3\n",
    "prob += x2<=7\n",
    "prob += 45*x1+60*x2<=600\n",
    "prob += 8*x1+12*x2 \n",
    "prob.solve()\n",
    "for v in prob.variables():\n",
    "    print(v.name,\"=\", v.varValue)\n",
    "print(\"Total Cost = \", value(prob.objective))"
   ]
  }
 ]
}