We are concerned with minimizing the cost of cleanup. Cost is a piecewise function, one for 0-14 days, and one for 15 days or more. Our variables crews = number of outside crews hired t = number of days for cleanup cost = total cost of cleanup time is related to crews with the following equation PkkidEc2IiwkLUkiXkc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiRJK1JlYWxEb21haW5HNiRGKUkoX3N5c2xpYkdGJDYkLCYiIiYiIiJJJmNyZXdzR0YkRjEhIiIiJSs5

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because it takes each crew 1 week to clean up 5 miles of coast line, and there are 200 mile of coast. LUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC9JInRHRiciIzlJJmNyZXdzR0Yn

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print(); # input placeholder

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The dividing line for time between the two functions is 14 days, we need to find what this is in terms of crews. This will mean we need 19 crews. So our piecewise function in terms of crews is divided between 0-19 for cost with penalty, and 19 to infinity for cost without penalty. JSFH We will examine the cost with penalty first. PkkmY29zdHBHNiIsKkkmY3Jld3NHRiQiJishPSomLUkiKkclKnByb3RlY3RlZEc2JCIkKyksJCokLCYiIiYiIiJGJkYxISIiIiUrOUYyRiZGMkYyLUYqNiQiJCsmRi5GMi1GKjYkIiYrKyIsJkYvRjQhIzlGMkYy

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

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The minimum cost for this function will therefore be $508,333.33 LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMtSSVzdWJzR0YkNiQvSSZjcmV3c0c2IiIjNkkidEdGKw==

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print(); # input placeholder

JCIrTExMTEIhIik=

This cleanup will take 24 days. Now we turn to the function without penalty. PkknY29zdG5wRzYiLChJJmNyZXdzR0YkIiYrIT0tSSIqRyUqcHJvdGVjdGVkRzYkIiQrJiwkLUkiXkc2JEYqL0krbW9kdWxlbmFtZUdGJEkrUmVhbERvbWFpbkc2JEYqSShfc3lzbGliR0YkNiQsJiIiJiIiIkYmRjghIiIiJSs5RjkqJi1GKTYkIiQrKUYtRjlGJkY5Rjk=

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print(); # input placeholder

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print(); # input placeholder

IicrPWM=

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%;

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%;

We know this is the minimum, since more crews will only create more cost. So the second function without penalty has a minimum of $561,800. This means our overall minum of the piecewise function is $508,333.33, the company should hire 11 additional crews. Also, we notice that our first function (with penalty) is equal to the second function when crews = 19, i.e., our piecewise function will be continuous, so we can ignore the second function in future evaulations. We only need to calculate that dividing point, and make sure our minimization is less than that point.