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@ojdo
Created June 29, 2016 11:31
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{
"cells": [
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "import matplotlib.pyplot as plt\nimport numpy as np\n%matplotlib inline",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "Q_B = np.linspace(0, 30)",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "S_B1 = 150./Q_B + 5 # S_B >= 5 + 150/Q_B\nS_B2 = 0.*Q_B + 10 # S_B >= 10 (redundant)\nS_B3 = 100./Q_B + 20 # S_B <= 20 + 100/Q_B\nS_B4 = 15 - 150./Q_B # S_B >= 15 - 150/Q_B (redundant)",
"execution_count": 3,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "S_Bs = np.stack((S_B1, S_B2, S_B3, S_B4), axis=1) # horizontal concatenation",
"execution_count": 4,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "plt.plot(Q_B, S_Bs) # plot all criteria\nplt.ylim(-5,100)\nplt.title('Criteria for S_B over Q_B: only S_B1 (blue) and S_B3 (red) are binding')",
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "<matplotlib.text.Text at 0x16d440da0>"
},
"metadata": {},
"execution_count": 5
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x16d1229e8>",
"image/png": 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nzmjYsGH64osvTNfLwujGjRs6cuSI6tata1r2/fffa+HChSlmfweQM6Xbk3r6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\nVgAAAABJRU5ErkJggg==\n"
},
"metadata": {}
}
]
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"pygments_lexer": "ipython3",
"codemirror_mode": {
"version": 3,
"name": "ipython"
},
"name": "python",
"version": "3.5.1",
"mimetype": "text/x-python",
"file_extension": ".py",
"nbconvert_exporter": "python"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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