The cost for operating a commercial truck is knv1/2 where k is a constant of pro

Question

The cost for operating a commercial truck is knv1/2 where k is a constant of proportionally, v is velocity in miles per hours, and n is the trip length in miles. It is estimated that at 85 mph, the average cost of operation is $52 per mile. The truck owner wants to minimize the cost of operation, which needs to balance against the cost of delays and unscheduled maintenance, which is assumed to be 10 per hour. What is the optimum velocity needed to minimize the total costs?

Explanation / Answer

let c be cost of operation c=knv^0.5 (c/n) is the cost of operation per mile=52 and velocity is taken as 85 that gives 'k' as 5.640 (n/v) gives the number of hours involved in the journey extra cost for each hour is 10 ----->total extra cost is (n/v)*10 total operation price is knv^0.5+(n/v)*10 to minimize this function derive it with respect to v and equating it to zero gives 'v'

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