A manufacturer incurs the following costs in producing x water ski vests in one

Question

A manufacturer incurs the following costs in producing x water ski vests in one day for 0<x<200: fixed costs, $245; unit production cost, $20 per vest; equipment maintenance and repairs, 0.05x^2 dollars. So the cost of manufacturing x vests in one given day is given by c(x)=0.05x^2+20x+245, where 0<x<200.

a.) what is the average cost per vest if x vests are produced in one day?

b.) Find the critical values of c(x), the intervals on which the average cost per vest is decreasing, the intervals on which the average cost per vest is increasing, and the local extrema.

Explanation / Answer

c(x)=0.05x^2+20x+245

For average cost

c(x)/x = 0.05x + 20 + 245/x

Critical values of c(x):

dc/dx = 0.1x + 20 = 0

=> x = -200

For average cost, 0.05 - 245/x^2 = 0

=> x = 70

Thus for 0<x<70, average cost per vest is decreasing,

For 70<x<200 average cost per vest is increasing

Local extrema = 70

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