Question

In: Math

The daily cost of producing x high performance wheels for racing is given by the following...

The daily cost of producing x high performance wheels for racing is given by the following function, where no more than 100 wheelscan be produced each day. What production level will give the lowest average cost per wheel? What is the minimum average cost?

C(x)=0.09x^3 - 4.5x^2 + 171x;(0,100]

what production level will give the lowest average cost per wheel?

x=_

Solutions

Expert Solution

we have,

we know that average cost is given by,

Hence,

we can write,

equate it to 0 we can say that,

Hence we can say that x = 25 is the critical point of average cost function

we have to find the production level x that will give the minimum average cost given that x must be in a range of (0, 100] means it can not be 0 but it can be 100 or less than 100

we have,

Evaluate the average cost function at x = 25 and x = 100

we can write,

we can see that average cost is minimum at x = 25

Hence we can say that production level of x = 25 per wheel will give lowest average cost per wheel and minimum average cost is $114.75

milcah answered 1 year ago

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