{
"cells": [
{
"cell_type": "markdown",
"id": "caa44533-7293-4ec6-af3d-c6aca35b43fc",
"metadata": {},
"source": [
"1. An oil spill has fouled 200 miles of Pacific shoreline.\n",
" The oil company responsible has been given 14 days to\n",
" clean up the shoreline, after which a fine will be levied\n",
" in the amount of \\\\$10,000/day. The local cleanup crew\n",
" can scrub five miles of beach per week at a cost of \n",
" \\\\$500/day. Additional crews can be brought in at a cost\n",
" of \\\\$18,000 plus \\\\$800/day for each crew."
]
},
{
"cell_type": "markdown",
"id": "7bf207e9-d657-4e51-a5de-1d1fc876545f",
"metadata": {},
"source": [
"(i) Let $T(n)$ be the number of days needed to clean the shoreline\n",
"expressed as a function $n$ of the number of additional crews hired.\n",
"Write an expression for $T(n)$."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "2e07477e-a893-4760-9042-ac4b44e341cd",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1-element Vector{Num}:\n",
" n"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Symbolics\n",
"D(f,x)=expand_derivatives(Differential(x)(f))\n",
"@variables n"
]
},
{
"cell_type": "markdown",
"id": "bb0a5295-dbc3-44d2-a726-b92eef2e85e6",
"metadata": {},
"source": [
"Given $n$ additional crews, the total number of crews working\n",
"is $n+1$. We assume each crew can scrub five miles of beach\n",
"per week, so with $n$ additional crews $5(n+1)$ miles of beach\n",
"per week can be cleaned. Since there are $7$ days in a week,\n",
"it follows that the cleanup rate $R(n)$ is miles/day is given by\n",
"$$\n",
" R(n)=5(n+1)\\,{{\\rm miles}\\over{\\rm week}} \\times {1\\over 7}\\,{{\\rm week}\\over{\\rm day}}\n",
" ={5\\over 7}(n+1)\\,{{\\rm miles}\\over{\\rm day}}.\n",
"$$\n",
"Since there are $200$ miles that need to be cleaned then the\n",
"total number of days needed to clean the spill is\n",
"$$\n",
" T(n)={200\\over R(n)} = {280\\over n+1}\\,{\\rm days}.\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "be49f15b-3dd1-4f93-a81e-74fe696345b3",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\u001b[96m280\u001b[39m / (\u001b[96m1\u001b[39m + n)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T(n)=7*200/(5*(n+1))\n",
"T(n)"
]
},
{
"cell_type": "markdown",
"id": "6eb63635-e95e-413e-a1ac-52d4e0988048",
"metadata": {},
"source": [
"(ii) Let the set $I_1=\\{\\, n : T(n)\\le 14\\, \\}$ be the choices of $n$\n",
"which avoid a fine and let\n",
"$I_2=\\{ n : T(n)>14\\}$ be the choices which lead to a fine.\n",
"Find $I_1$ and $I_2$.\n"
]
},
{
"cell_type": "markdown",
"id": "3a158a73-5c64-4a6e-8279-aaeda4dec2cc",
"metadata": {},
"source": [
"To find $I_1$ write\n",
"$$\n",
" {280\\over n+1}\\le 14\n",
"\\qquad\\hbox{so that}\\qquad\n",
" n+1\\ge {280\\over 14}=20.\n",
"$$\n",
"It follows that $n\\ge 19$ and so $I_1=\\big\\{\\, 19, 20, 21, \\ldots,\\,\\big\\}$.\n",
"\n",
"To find $I_2$ note $I_1$ and $I_2$ are disjoint and $I_1\\cup I_2=\\{0\\}\\cup{\\bf N}$.\n",
"\n",
"Therefore $I_2=\\{0\\}\\cup {\\bf N}\\setminus I_1=\\big\\{\\, 0,1,\\ldots, 18\\,\\big\\}$."
]
},
{
"cell_type": "markdown",
"id": "9f6b64c0-92b8-4c67-aa88-1b615d183002",
"metadata": {},
"source": [
"(iii) The total cost of the cleanup is\n",
"$$C(n) = \\underbrace{(500 +800n)T(n)}_{\\hbox{daily costs}}\n",
" + \\underbrace{18000n\\vphantom{)}}_{\\hbox{crew setup}}\n",
" + \\underbrace{F(n)}_{\\hbox{fine}}$$\n",
"where the fine is given by\n",
"$$\\eqalign{\n",
" F(n)\n",
" =\\cases{\n",
" 0 & for $n\\in I_1$\\cr\n",
" 10000\\big(T(n)-14\\big) & for $n\\in I_2$.\n",
" }\n",
"}$$\n",
"Plot the points $(n,C(n))$ for the $n=0,1,\\ldots,20$.\n"
]
},
{
"cell_type": "markdown",
"id": "ed5d18c6-f5aa-4d48-883c-018421a59895",
"metadata": {},
"source": [
"Hint: In Julia one can\n",
"define `F(n)=10000*max(T(n)-14,0)`\n",
"and use the `scatter` command in the `Plots` library\n",
"for plotting points."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f1a0ec37-d361-4b19-b777-69dec11c675c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\u001b[96m10000\u001b[39mmax(-\u001b[96m14\u001b[39m + \u001b[96m280\u001b[39m / (\u001b[96m1\u001b[39m + n), \u001b[96m0\u001b[39m)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"F(n)=10000*max(T(n)-14,0)\n",
"F(n)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "eb57b9a0-0e13-4d3a-99e3-0c634f0b6224",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\u001b[96m18000\u001b[39mn + \u001b[96m10000\u001b[39mmax(-\u001b[96m14\u001b[39m + \u001b[96m280\u001b[39m / (\u001b[96m1\u001b[39m + n), \u001b[96m0\u001b[39m) + (\u001b[96m280\u001b[39m(\u001b[96m500\u001b[39m + \u001b[96m800\u001b[39mn)) / (\u001b[96m1\u001b[39m + n)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"C(n)=(500+800n)*T(n)+18000*n+F(n)\n",
"C(n)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "3247946d-50ed-49fc-800e-d2e7929781eb",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Plots\n",
"scatter(n->n,n->C(n),0:20,\n",
" xlabel=\"n\",ylabel=\"C(n)\",title=\"Cost of Cleanup vs Additional Crews\",legend=false)"
]
},
{
"cell_type": "markdown",
"id": "bb2f5e9b-024f-4ea2-b925-b99b913e961a",
"metadata": {},
"source": [
"(iv) Compute $C(n)$ for $n=0,\\ldots,20$\n",
" and determine the optimal value for $n$.\n",
"\n",
"Hint: $n=11$ is\n",
"optimal but include a table of all 21 values\n",
"of $n$ and $C(n)$."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "5359abf3-26f1-44f5-b790-a38749bc58b5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"21×4 Matrix{Float64}:\n",
" 0.0 280.0 2.66e6 2.8e6\n",
" 1.0 140.0 1.26e6 1.46e6\n",
" 2.0 93.3333 7.93333e5 1.02533e6\n",
" 3.0 70.0 560000.0 817000.0\n",
" 4.0 56.0 420000.0 699200.0\n",
" 5.0 46.6667 3.26667e5 6.26667e5\n",
" 6.0 40.0 260000.0 580000.0\n",
" 7.0 35.0 210000.0 549500.0\n",
" 8.0 31.1111 1.71111e5 5.29778e5\n",
" 9.0 28.0 140000.0 517600.0\n",
" 10.0 25.4545 1.14545e5 5.10909e5\n",
" 11.0 23.3333 93333.3 5.08333e5\n",
" 12.0 21.5385 75384.6 5.08923e5\n",
" 13.0 20.0 60000.0 512000.0\n",
" 14.0 18.6667 46666.7 5.17067e5\n",
" 15.0 17.5 35000.0 523750.0\n",
" 16.0 16.4706 24705.9 5.31765e5\n",
" 17.0 15.5556 15555.6 5.40889e5\n",
" 18.0 14.7368 7368.42 5.50947e5\n",
" 19.0 14.0 0.0 561800.0\n",
" 20.0 13.3333 0.0 580000.0"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Include the time T(n) and fine F(n) for better understanding\n",
"A=vcat([[n T(n) F(n) C(n)] for n=0:20]...)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "7611e744-762e-46cb-a4fc-992365af739e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"┌─────┬────────┬────────────┬────────────┐\n",
"│\u001b[1m n \u001b[0m│\u001b[1m T(n) \u001b[0m│\u001b[1m F(n) \u001b[0m│\u001b[1m C(n) \u001b[0m│\n",
"├─────┼────────┼────────────┼────────────┤\n",
"│ 0 │ 280.00 │ 2660000.00 │ 2800000.00 │\n",
"│ 1 │ 140.00 │ 1260000.00 │ 1460000.00 │\n",
"│ 2 │ 93.33 │ 793333.33 │ 1025333.33 │\n",
"│ 3 │ 70.00 │ 560000.00 │ 817000.00 │\n",
"│ 4 │ 56.00 │ 420000.00 │ 699200.00 │\n",
"│ 5 │ 46.67 │ 326666.67 │ 626666.67 │\n",
"│ 6 │ 40.00 │ 260000.00 │ 580000.00 │\n",
"│ 7 │ 35.00 │ 210000.00 │ 549500.00 │\n",
"│ 8 │ 31.11 │ 171111.11 │ 529777.78 │\n",
"│ 9 │ 28.00 │ 140000.00 │ 517600.00 │\n",
"│ 10 │ 25.45 │ 114545.45 │ 510909.09 │\n",
"│ 11 │ 23.33 │ 93333.33 │ 508333.33 │\n",
"│ 12 │ 21.54 │ 75384.62 │ 508923.08 │\n",
"│ 13 │ 20.00 │ 60000.00 │ 512000.00 │\n",
"│ 14 │ 18.67 │ 46666.67 │ 517066.67 │\n",
"│ 15 │ 17.50 │ 35000.00 │ 523750.00 │\n",
"│ 16 │ 16.47 │ 24705.88 │ 531764.71 │\n",
"│ 17 │ 15.56 │ 15555.56 │ 540888.89 │\n",
"│ 18 │ 14.74 │ 7368.42 │ 550947.37 │\n",
"│ 19 │ 14.00 │ 0.00 │ 561800.00 │\n",
"│ 20 │ 13.33 │ 0.00 │ 580000.00 │\n",
"└─────┴────────┴────────────┴────────────┘\n"
]
}
],
"source": [
"# Make a nicer table (optional)\n",
"using PrettyTables\n",
"pretty_table(A,\n",
" formatters=[fmt__printf(\"%3d\",[1]),fmt__printf(\"%.2f\",[2,3,4])],\n",
" column_labels=[\"n\",\"T(n)\",\"F(n)\",\"C(n)\"])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c1ceb5dc-f7ae-437e-9506-7ef42afc58ed",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"11.0"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nopt=A[argmin(A[:,4])]"
]
},
{
"cell_type": "markdown",
"id": "7969ab9f-63b9-496f-8425-6ecfd89200d6",
"metadata": {},
"source": [
"The optimal number of additional crews is $n=11$."
]
},
{
"cell_type": "markdown",
"id": "2c9b388c-1abb-4249-8f1b-91ca8eafb840",
"metadata": {},
"source": [
"The company has filed an appeal on grounds that the fine\n",
"of \\\\$10,000/day for missing the deadline is excessive.\n",
"Let $M$ be the daily fine. What is the least value for\n",
"$M$ that ensures the cost-optimized value of $T(n)$ meets\n",
"the 14 day deadline?\n",
"Is $M$ larger or smaller than \\\\$10,000/day?"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "f1eb2ed5-7088-48eb-a473-34034040bd1e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"93333.33333333333"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"F(nopt)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "454c4f95-78ac-4760-935f-350cfcd00227",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"23.333333333333332"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T(nopt)"
]
},
{
"cell_type": "markdown",
"id": "6114c3a5-8f1a-4ac7-aaee-9b27d6c027e4",
"metadata": {},
"source": [
"The fine and time of cleanup at the optimal value of $n$ is\n",
"$$\n",
" F(n_{\\rm opt})\\approx 93333.33\n",
"\\qquad\\hbox{and}\\qquad\n",
" T(n_{\\rm opt})\\approx 23.33.\n",
"$$\n",
"Thus, the fine of \\\\$10000/day was not enough to avoid missing the deadline."
]
},
{
"cell_type": "markdown",
"id": "27d4d6cd-b16a-41ee-b104-c15dfd947a7a",
"metadata": {},
"source": [
"For no fine we have $n\\in I_1$, thus the fewest additional\n",
"work crews needed is $19$ to avoid the fine. Let $M$ be the\n",
"daily fine"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "49ee1a27-7352-4525-bdb4-385fb7a04a34",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\u001b[96m18000\u001b[39mn + (\u001b[96m280\u001b[39m(\u001b[96m500\u001b[39m + \u001b[96m800\u001b[39mn)) / (\u001b[96m1\u001b[39m + n) + M*max(-\u001b[96m14\u001b[39m + \u001b[96m280\u001b[39m / (\u001b[96m1\u001b[39m + n), \u001b[96m0\u001b[39m)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@variables M\n",
"F(n)=M*max(T(n)-14,0)\n",
"C(n)"
]
},
{
"cell_type": "markdown",
"id": "b60339b8-e4ac-4621-a6c8-1147f2448fcd",
"metadata": {},
"source": [
"What we now seek is the minimum value of $M$ when $C(19)