{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Monte Carlo simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our goal is to estimate our profit $P$ based on the following variable\n",
    "- $V$ - volume of production (number of produced units)\n",
    "- $p$ - price of one unit\n",
    "- $fc$ - fixed cost\n",
    "- $vc$ - variable cost\n",
    "\n",
    "using the formula $P = V\\cdot (p-vc)-fc$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each variable, we have received three estimation - minimum, best guess and maximum:\n",
    "\n",
    "$V=(10\\,000; 40\\, 000; 100\\,000)$\n",
    "\n",
    "$p=(100; 110; 150)$\n",
    "\n",
    "$fc=(140\\,000; 300\\, 000; 420\\,000)$\n",
    "\n",
    "$vc=(10; 30; 105)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the calculation we will use Monte Carlo simulation method and we will use triangular probability distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "n =\n",
      "\n",
      "    10000000\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%number of simulation\n",
    "n=10000000\n",
    "\n",
    "%Firstly, we will construct individual probability distributions \n",
    "\n",
    "%probability distribution (pd) of Volume\n",
    "V_pd = makedist('Triangular','A',10000,'B',40000,'C',100000);\n",
    "\n",
    "%probability distribution (pd) of Price\n",
    "p_pd = makedist('Triangular','A',100,'B',110,'C',150);\n",
    "\n",
    "%probability distribution (pd) of Fixed cost\n",
    "fc_pd = makedist('Triangular','A',140000,'B',300000,'C',420000);\n",
    "\n",
    "%probability distribution (pd) of variable cost\n",
    "vc_pd = makedist('Triangular','A',10,'B',30,'C',105);\n",
    "\n",
    "%to obtain n random values of volume, we will use\n",
    "V=random(V_pd,1,n);\n",
    "\n",
    "%similar approach will be applied on remaining variables\n",
    "p=random(p_pd,1,n);\n",
    "fc=random(fc_pd,1,n);\n",
    "vc=random(vc_pd,1,n);\n",
    "\n",
    "%we will apply the whole formula to obtain n possible results\n",
    "P=p.*(V-vc)-fc;\n",
    "\n",
    "%and we will plot the results\n",
    "hist(P,100)\n",
    "xlim([0,15000000]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets make a deeper look into the computation. What will happen, if we do only one simulation? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "n =\n",
      "\n",
      "     1\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=1\n",
    "\n",
    "%to obtain n random values of volume, we will use\n",
    "V=random(V_pd,1,n);\n",
    "\n",
    "%similar approach will be applied on remaining variables\n",
    "p=random(p_pd,1,n);\n",
    "fc=random(fc_pd,1,n);\n",
    "vc=random(vc_pd,1,n);\n",
    "\n",
    "%we will apply the whole formula to obtain n possible results\n",
    "P=p.*(V-vc)-fc;\n",
    "\n",
    "%and we will plot the results\n",
    "hist(P,100)\n",
    "xlim([0,15000000]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%to obtain n random values of volume, we will use\n",
    "V=random(V_pd,1,n);\n",
    "\n",
    "%similar approach will be applied on remaining variables\n",
    "p=random(p_pd,1,n);\n",
    "fc=random(fc_pd,1,n);\n",
    "vc=random(vc_pd,1,n);\n",
    "\n",
    "%we will apply the whole formula to obtain n possible results\n",
    "P=p.*(V-vc)-fc;\n",
    "\n",
    "%and we will plot the results\n",
    "hist(P,100)\n",
    "xlim([0,15000000]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "n =\n",
      "\n",
      "     1\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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f+qtSqZRSymwWdKkHAPgfCAqSUqqtra2vry+ZTCqlAoGAw+EwHg4NDg729/fnl+XfdLhw4UJvb++NN95oXF0BAMqXrAsLl8s1Pj7udDorKyurqqoCgYBxPBgMJhKJ/L9J+slPfnLx4sXVq1cnEomGhoYyemQHAFiMrCBpmrZgXY4cOTJ7969//WuxJgIAFImsW3YAgC8tggQAEIEgAQBEIEgAABEIEgBABIIEABCBIAEARCBIAAARCBIAQASCBAAQgSABAEQgSAAAEQgSAEAEggQAEIEgAQBEIEgAABEIEgBABIIEABCBIAEARCBIAAARCBIAQASCBAAQgSABAEQwl3qAuSKRyMDAgK7rra2tLS0tl14cDAbfe++97du322y24owHAFgmsq6QwuFwe3t7dXV1Q0OD1+vt7++/xOJYLPbTn/70oYce+uCDD4o2IQBgmcgKks/n6+jocLlcd9555+HDh30+XzabXWzxgQMH3G53MccDACwfWUEaGRlpamoytpubm1Op1Ojo6IIr//SnPymlduzYUbzhAADLSdAzJF3XM5lMXV2dsWsymaxWazwen7/yk08+efzxx//whz9c9nva7XZjo7u7m8spAF82fr+/t7e31FMslaAgzczMKKVmv55gNpsXvGXn9Xrvvvvu6urqdDp96e8ZDocLOyQAlBG3253/XTz/C7pYgm7ZaZqmlAqFQvkj09PTFotlzrJTp06dPn36a1/72tDQ0PDwsFLq7bfffvfdd4s5KgCg4ARdIWmaVltbG41Gjd1YLKbren19/ZxlJpNpy5Ytzz77rFIql8sppd54442rrrpq/koAQBkRFCSlVFtbW19f33e+851Vq1YFAgGHw2E8UhocHEwmk11dXUqpxsbGxsZGY306nd6yZcsDDzyQPwIAKFOyguRyucbHx51OZ2VlZVVVVSAQMI4Hg8FEImEECQCwIskKkqZpC74QcuTIkcXW89oCAKwMgl5qAAB8mREkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAggrnUA8wViUQGBgZ0XW9tbW1paVlwzZkzZ958883JyUmz2bx9+/bvfe97RR4SAFBwsq6QwuFwe3t7dXV1Q0OD1+vt7+9fcNmbb775n//855Zbblm3bt2hQ4cOHz5c5DkBAAUn6wrJ5/N1dHS4XC6lVE1Njcfj6ezsrKiomLOsp6cnv33dddft37//wIEDRR0UAFBosq6QRkZGmpqajO3m5uZUKjU6OnrpL0kkEuvWrVv+0QAAy0vQFZKu65lMpq6uztg1mUxWqzUejy+4eGxsbHBwMB6Pf/jhhz6fr3hTAgCWh6ArpJmZGaWUzWbLHzGbzdlsdsHFa9as2bp167p16/7973///e9/X+x72j/j9/sLPjAACOf3+/M/Bks9y+UJukLSNE0pFQqFGhsbjSPT09MWi2XBxevXr1+/fr1SaufOne3t7Tt27JhdsrxwOLxs8wKAdG632+12G9vymyToCknTtNra2mg0auzGYjFd1+vr6y/9VcaC999/f9nnAwAsJ0FBUkq1tbX19fUlk0mlVCAQcDgcxiOlwcHB2a+A5990yGazv/zlL6+55pr8RRUAoEwJumWnlHK5XOPj406ns7KysqqqKhAIGMeDwWAikejq6jJ2Dx48GI1GV69ePTU19X//93+/+c1vTCZZZQUAfF6ygqRpWm9v7/zjR44cmb174sSJYk0EACgSLiwAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIIK51APMFYlEBgYGdF1vbW1taWlZbM1rr732/vvvX3XVVTt37mxoaCjykACAgpN1hRQOh9vb26urqxsaGrxeb39//4LLOjo63n///VtuuUXTtL1797700ktFnhMAUHCyrpB8Pl9HR4fL5VJK1dTUeDyezs7OioqKOcveeOONq6++2tiuqqp66qmn2traij0rAKCgZF0hjYyMNDU1GdvNzc2pVGp0dHT+snyNlFI2my2dThdpPgDAshEUJF3XM5lMXV2dsWsymaxWazwev8SXpNPpo0eP7t69uxjzAQCWk6AgzczMKKVsNlv+iNlszmazl/iS+++//6tf/apxi29B9s/4/f4CjgoAZcHv9+d/DJZ6lssT9AxJ0zSlVCgUamxsNI5MT09bLJbF1j/wwAMfffTRM888M/8hU144HC74nABQLtxut9vtNrblN0lWkGpra6PRqLEbi8V0Xa+vr19w8f79+//xj3/8/ve/t1qtRZwRALBcBN2yU0q1tbX19fUlk0mlVCAQcDgcxiOlwcHB2a+AHzhwYGxs7Omnn7ZYLOl0mpcaAGAFEHSFpJRyuVzj4+NOp7OysrKqqioQCBjHg8FgIpHo6uoydp9//nml1LZt24zdK6+8cmxsrCQDAwAKRVaQNE3r7e2df/zIkSOzd3kyBAArj6xbdgCALy2CBAAQgSABAEQgSAAAEQgSAEAEggQAEIEgAQBEIEgAABEIEgBABIIEABCBIAEARCBIAAARCBIAQASCBAAQgSABAEQgSAAAEQgSAEAEggQAEIEgAQBEIEgAABEIEgBABIIEABCBIAEARCBIAAARzKUeYK5IJDIwMKDremtra0tLy4JrcrlcMBicmJjIZDK7d+8u8oQAgOUgK0jhcHjPnj379u1bu3at1+udnJzs6uqav+zhhx8+fvz4pk2bQqEQQQKAlUHWLTufz9fR0eFyue68887Dhw/7fL5sNjt/2SOPPHL69On77ruv+BMCAJaJrCCNjIw0NTUZ283NzalUanR0dP4yTdOKOxcAYNkJCpKu65lMpq6uztg1mUxWqzUej3+R72n/jN/vL8CIAFBW/H5//sdgqWe5PEHPkGZmZpRSNpstf8RsNi94y27pwuHwFx0LAMqW2+12u93GtvwmCbpCMm7EhUKh/JHp6WmLxVK6iQAAxSMrSLW1tdFo1NiNxWK6rtfX15d2KgBAcQgKklKqra2tr68vmUwqpQKBgMPhMB4pDQ4O9vf355flcrl0Om3czUun0+l0ukTzAgAKRtAzJKWUy+UaHx93Op2VlZVVVVWBQMA4HgwGE4lE/t8kHT9+vKenx9jesmWLUurs2bO8egcAZe0K41WCFclut/NSAz4X423M/ENgYCWR/yNR1i07AMCXFkECAIhAkAAAIhAkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAilGuQIpHIwYMH9+/f//rrr5d6FhSG3+8v9Qj4fPjIUFhlGaRwONze3l5dXd3Q0OD1evv7+0s9EQqgt7e31CPg8+EjQ2GZSz3A/8Ln83V0dLhcLqVUTU2Nx+Pp7OysqKgo9VwAgP9dWV4hjYyMNDU1GdvNzc2pVGp0dLS0IwEAvqDyu0LSdT2TydTV1Rm7JpPJarXG4/H5K51Op91uL+pw+GKEfF7ciVo6IR8ZlsLpdJZ6hMsovyDNzMwopWw2W/6I2WzOZrPzVx49erR4YwEAvpjyu2WnaZpSKhQK5Y9MT09bLJbSTQQAKICyDFJtbW00GjV2Y7GYruv19fWlnQoA8AWVX5CUUm1tbX19fclkUikVCAQcDkf+kRIAoEyV3zMkpZTL5RofH3c6nZWVlVVVVYFAoNQTAQC+qCuMdwQAACitsrxlBwBYeQgSAECEsnyGdFmRSGRgYEDX9dbW1paWllKPg8s4ffr0+fPn87s333zzhg0bSjcOFpDL5YLB4MTERCaT2b179+z/idNNpsU+Msmn2woMUjgc3rNnz759+9auXev1eicnJ7u6uko9FC7l5ZdfPnXqlMPhMHY3btwo5wyB4eGHHz5+/PimTZtCodDsn26cbmIt9pFJPt1W4EsN995778aNG/fv36+UGhoa8ng8b731Fn96VbIDBw4opQ4fPlzqQbCodDqtadrQ0FB3d/fY2Fj+OKebWIt9ZJJPtxX4DIk/vVqOksnk8PDwuXPnSj0IFmb8hZT5ON3EWuwjU4JPt5V2y27pf3oVorz22msTExPnzp2rrq5++umn+ZfOZYHTrUyJPd1W2hXS0v/0KuTweDzvvPPOs88+e/r06euvv767u7vUE2FJON3KkeTTbaUFiT+9Wo7yP9E0TXO5XJFIRNf10o6EpeB0K0eST7cVGCT+9GpZS6VSSimzeaXdTF6RON3KnbTTbaUFSfGnV8tQ/jH4hQsXent7b7zxxks8j0VJ5HK5dDpt3I5Lp9PpdNo4zukm1mIfmeTTbQW+9p1Op3t6eoaHh/N/enX9+vWlHgqXctttt128eHH16tWJRKKhoeFXv/pVdXV1qYfC/+fVV1/t6emZfeTs2bOapnG6ibXYRyb5dFuBQTJcvHjx008/5dwoF+l0+uzZs1u2bJHzyxqWjtOtvIg93VZskAAA5WUFPkMCAJQjggQAEIEgAQBEIEgAABEIEgBABIIEACvZ1NTUhQsXSj3Fkkj5ixEAgMK6ePFiT0/PRx99dM0113zlK1/59a9/XeqJLoN/hwQAK9P+/fvXr18v6u95XxpBAoAVKJ1ONzQ0/O1vf3vrrbfWrVtnt9tLPdHlccsOAFagM2fOaJp21113bdq06dy5czfddNOhQ4dKPdRlECQAKAO5XC4YDE5MTGQymd27d8/+nyKRyMDAgK7rra2tLS0txsFUKpVIJB588MGbbropmUxu27Zt79691113XSlmXyresgOAMvDwww/v27fv2WefPXjw4Ozj4XC4vb29urq6oaHB6/X29/cbx7du3aqU2rJli1Jq1apVW7du/ec//1n0qT8fniEBQBlIp9Oapg0NDXV3d4+NjeWP33vvvRs3bty/f79SamhoyOPxvPXWWxUVFUqpXbt2eTye7du3f/LJJ9u3bz9x4sS1115bsv8DS8AVEgCUXi6Xe/fdd2cfmZyc/O9//5vfXew/FTEyMtLU1GRsNzc3p1Kp/H+C79FHH/35z39+3333tbe3P/jgg8JrpHiGBAASmEymv/zlL9/61rduuukmpdTk5OTRo0eN655L0HU9k8nk/yu9JpPJarXG43Fjt76+/sSJE1NTU6tWrTKumYQjSAAggsfjeeKJJ5RSNpttKTVSShnPXGw2W/6I2Ww2/rPleVartdCTLhdu2QGAFB6P59VXX33yySeXUiP12X28UCiUPzI9PW2xWJZrvmVGkABAivPnz+dyuQ0bNpw5c2Yp6zVNq62tjUajxm4sFtN1vb6+fjlnXEYECQBEOH/+/MDAwEMPPXTPPfeMjo7OaVIul0un08btuHQ6nU6njeNtbW19fX3JZFIpFQgEHA5H/pFS2eG1bwAovVwu5/P5HnjggfyRJ5988gc/+MHVV19t7L766qs9PT2zv+Ts2bOapqXT6Z6enuHh4crKyqqqqkAgsH79+qKOXjgECQDK3sWLFz/99NPyTZGBIAEAROAZEgBABIIEABCBIAEARCBIAAAR/h96SekTsnQR1QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=1\n",
    "\n",
    "%to obtain n random values of volume, we will use\n",
    "V=random(V_pd,1,n);\n",
    "\n",
    "%similar approach will be applied on remaining variables\n",
    "p=random(p_pd,1,n);\n",
    "fc=random(fc_pd,1,n);\n",
    "vc=random(vc_pd,1,n);\n",
    "\n",
    "%we will apply the whole formula to obtain n possible results\n",
    "P=p.*(V-vc)-fc;\n",
    "\n",
    "%and we will plot the results\n",
    "hist(P,100)\n",
    "xlim([0,15000000]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the output is random. Lets try 100 simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "n =\n",
      "\n",
      "   100\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=100\n",
    "\n",
    "%to obtain n random values of volume, we will use\n",
    "V=random(V_pd,1,n);\n",
    "\n",
    "%similar approach will be applied on remaining variables\n",
    "p=random(p_pd,1,n);\n",
    "fc=random(fc_pd,1,n);\n",
    "vc=random(vc_pd,1,n);\n",
    "\n",
    "%we will apply the whole formula to obtain n possible results\n",
    "P=p.*(V-vc)-fc;\n",
    "\n",
    "%and we will plot the results\n",
    "hist(P,100)\n",
    "xlim([0,15000000]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is closer to the expected distribution - lets change the number of bins in histogram to 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "n =\n",
      "\n",
      "   100\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=100\n",
    "\n",
    "%to obtain n random values of volume, we will use\n",
    "V=random(V_pd,1,n);\n",
    "\n",
    "%similar approach will be applied on remaining variables\n",
    "p=random(p_pd,1,n);\n",
    "fc=random(fc_pd,1,n);\n",
    "vc=random(vc_pd,1,n);\n",
    "\n",
    "%we will apply the whole formula to obtain n possible results\n",
    "P=p.*(V-vc)-fc;\n",
    "\n",
    "%and we will plot the results\n",
    "hist(P,10)\n",
    "xlim([0,15000000]);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Matlab",
   "language": "matlab",
   "name": "matlab"
  },
  "language_info": {
   "codemirror_mode": "octave",
   "file_extension": ".m",
   "help_links": [
    {
     "text": "MetaKernel Magics",
     "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "matlab",
   "version": "0.16.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}