yogabonito/guinness.ipynb

## guinness.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hell = {\"mais\": 2,\n",
    "        \"gerste\": 14,\n",
    "        \"gewinn\": 30\n",
    "}\n",
    "dunkel = {\n",
    "    \"mais\": 5,\n",
    "    \"gerste\": 10,\n",
    "    \"gewinn\": 40\n",
    "}\n",
    "restriktion = {\n",
    "    \"mais\": 100,\n",
    "    \"gerste\": 280\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### wie viel Fässer dunkles Bier gehen sich mit dem Mais bzw. der Gerste maximal aus?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fässer_dunkel_mais = restriktion[\"mais\"] / dunkel[\"mais\"]\n",
    "fässer_dunkel_mais"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fässer_dunkel_gerste = restriktion[\"gerste\"] / dunkel[\"gerste\"]\n",
    "fässer_dunkel_gerste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12.,\n",
       "       13., 14., 15., 16., 17., 18., 19., 20.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "achse_dunkel_mais = np.arange(fässer_dunkel_mais + 1)\n",
    "achse_dunkel_mais"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12.,\n",
       "       13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,\n",
       "       26., 27., 28.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "achse_dunkel_gerste = np.arange(fässer_dunkel_gerste + 1)\n",
    "achse_dunkel_gerste"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Restriktion für Mais"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$2 \\cdot hell + 5 \\cdot dunkel \\leq 100 \\Rightarrow hell \\leq \\frac{100}{2} - \\frac{5 \\cdot dunkel}{2} = 50 - \\frac{5}{2} \\cdot dunkel$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([50. , 47.5, 45. , 42.5, 40. , 37.5, 35. , 32.5, 30. , 27.5, 25. ,\n",
       "       22.5, 20. , 17.5, 15. , 12.5, 10. ,  7.5,  5. ,  2.5,  0. ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "restr_gerade_mais = 50 - 5/2 * achse_dunkel_mais\n",
    "restr_gerade_mais"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Restriktion für Gerste"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$14 \\cdot hell + 10 \\cdot dunkel \\leq 280 \\Rightarrow hell \\leq \\frac{280}{14} - \\frac{10 \\cdot dunkel}{14} = 20 - \\frac{5}{7} \\cdot dunkel$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20.  , 19.29, 18.57, 17.86, 17.14, 16.43, 15.71, 15.  , 14.29,\n",
       "       13.57, 12.86, 12.14, 11.43, 10.71, 10.  ,  9.29,  8.57,  7.86,\n",
       "        7.14,  6.43,  5.71,  5.  ,  4.29,  3.57,  2.86,  2.14,  1.43,\n",
       "        0.71,  0.  ])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "restr_gerade_gerste = 20 - 5/7 * achse_dunkel_gerste\n",
    "restr_gerade_gerste.round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Schnittpunkt in der Zeichnung (siehe unten)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$50 - \\frac{5}{2} \\cdot dunkel = 20 - \\frac{5}{7} \\cdot dunkel \\Rightarrow 30 = \\frac{5}{2} \\cdot dunkel - \\frac{5}{7} \\cdot dunkel = (\\frac{5}{2} - \\frac{5}{7}) \\cdot dunkel = (\\frac{35}{14} - \\frac{10}{14}) \\cdot dunkel = \\frac{25}{14} \\cdot dunkel \\approx 1.7857 \\cdot dunkel$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\Rightarrow dunkel = 30 / 1.7857 = 16.8$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\Rightarrow hell = 20 - 5/7 \\cdot dunkel = 20 - 5/7 \\cdot 16.8 = 8$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zeichnung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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RVDFhAlnAw126VkuVXkxO139zj9mzzW1NcKST01vufMPmrntT6Aq+WeeU68Mq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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe64cccb908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(achse_dunkel_mais, restr_gerade_mais)\n",
    "plt.plot(achse_dunkel_gerste, restr_gerade_gerste)\n",
    "plt.plot(achse_dunkel_gerste, np.ones(len(achse_dunkel_gerste)) * 8, linestyle='--', color=\"r\")\n",
    "plt.axvline(16.8, linestyle='--', color=\"r\")\n",
    "plt.xlim(0, 28)\n",
    "plt.ylim(0, 50)\n",
    "plt.savefig(\"guinness.png\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": false,
   "sideBar": false,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": false,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": [
	"%matplotlib inline"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": [
	"import numpy as np\n",
	"from matplotlib import pyplot as plt"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": [
	"hell = {\"mais\": 2,\n",
	" \"gerste\": 14,\n",
	" \"gewinn\": 30\n",
	"}\n",
	"dunkel = {\n",
	" \"mais\": 5,\n",
	" \"gerste\": 10,\n",
	" \"gewinn\": 40\n",
	"}\n",
	"restriktion = {\n",
	" \"mais\": 100,\n",
	" \"gerste\": 280\n",
	"}"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"### wie viel Fässer dunkles Bier gehen sich mit dem Mais bzw. der Gerste maximal aus?"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"20.0"
	]
	},
	"execution_count": 4,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"fässer_dunkel_mais = restriktion[\"mais\"] / dunkel[\"mais\"]\n",
	"fässer_dunkel_mais"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"28.0"
	]
	},
	"execution_count": 5,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"fässer_dunkel_gerste = restriktion[\"gerste\"] / dunkel[\"gerste\"]\n",
	"fässer_dunkel_gerste"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 6,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"array([ 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,\n",
	" 13., 14., 15., 16., 17., 18., 19., 20.])"
	]
	},
	"execution_count": 6,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"achse_dunkel_mais = np.arange(fässer_dunkel_mais + 1)\n",
	"achse_dunkel_mais"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 7,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"array([ 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,\n",
	" 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,\n",
	" 26., 27., 28.])"
	]
	},
	"execution_count": 7,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"achse_dunkel_gerste = np.arange(fässer_dunkel_gerste + 1)\n",
	"achse_dunkel_gerste"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"### Restriktion für Mais"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"$2 \\cdot hell + 5 \\cdot dunkel \\leq 100 \\Rightarrow hell \\leq \\frac{100}{2} - \\frac{5 \\cdot dunkel}{2} = 50 - \\frac{5}{2} \\cdot dunkel$"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 11,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"array([50. , 47.5, 45. , 42.5, 40. , 37.5, 35. , 32.5, 30. , 27.5, 25. ,\n",
	" 22.5, 20. , 17.5, 15. , 12.5, 10. , 7.5, 5. , 2.5, 0. ])"
	]
	},
	"execution_count": 11,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"restr_gerade_mais = 50 - 5/2 * achse_dunkel_mais\n",
	"restr_gerade_mais"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"### Restriktion für Gerste"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"$14 \\cdot hell + 10 \\cdot dunkel \\leq 280 \\Rightarrow hell \\leq \\frac{280}{14} - \\frac{10 \\cdot dunkel}{14} = 20 - \\frac{5}{7} \\cdot dunkel$"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 12,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"array([20. , 19.29, 18.57, 17.86, 17.14, 16.43, 15.71, 15. , 14.29,\n",
	" 13.57, 12.86, 12.14, 11.43, 10.71, 10. , 9.29, 8.57, 7.86,\n",
	" 7.14, 6.43, 5.71, 5. , 4.29, 3.57, 2.86, 2.14, 1.43,\n",
	" 0.71, 0. ])"
	]
	},
	"execution_count": 12,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"restr_gerade_gerste = 20 - 5/7 * achse_dunkel_gerste\n",
	"restr_gerade_gerste.round(2)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"### Schnittpunkt in der Zeichnung (siehe unten)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"$50 - \\frac{5}{2} \\cdot dunkel = 20 - \\frac{5}{7} \\cdot dunkel \\Rightarrow 30 = \\frac{5}{2} \\cdot dunkel - \\frac{5}{7} \\cdot dunkel = (\\frac{5}{2} - \\frac{5}{7}) \\cdot dunkel = (\\frac{35}{14} - \\frac{10}{14}) \\cdot dunkel = \\frac{25}{14} \\cdot dunkel \\approx 1.7857 \\cdot dunkel$"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"$\\Rightarrow dunkel = 30 / 1.7857 = 16.8$"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"$\\Rightarrow hell = 20 - 5/7 \\cdot dunkel = 20 - 5/7 \\cdot 16.8 = 8$"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"### Zeichnung"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 20,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"image/png": 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	"text/plain": [
	"<matplotlib.figure.Figure at 0x7fe64cccb908>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"plt.figure()\n",
	"plt.plot(achse_dunkel_mais, restr_gerade_mais)\n",
	"plt.plot(achse_dunkel_gerste, restr_gerade_gerste)\n",
	"plt.plot(achse_dunkel_gerste, np.ones(len(achse_dunkel_gerste)) * 8, linestyle='--', color=\"r\")\n",
	"plt.axvline(16.8, linestyle='--', color=\"r\")\n",
	"plt.xlim(0, 28)\n",
	"plt.ylim(0, 50)\n",
	"plt.savefig(\"guinness.png\")"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"language": "python",
	"name": "python3"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.5.2"
	},
	"toc": {
	"base_numbering": 1,
	"nav_menu": {},
	"number_sections": false,
	"sideBar": false,
	"skip_h1_title": false,
	"title_cell": "Table of Contents",
	"title_sidebar": "Contents",
	"toc_cell": false,
	"toc_position": {},
	"toc_section_display": false,
	"toc_window_display": false
	}
	},
	"nbformat": 4,
	"nbformat_minor": 2
	}