The daily cost of producing x high performance wheels for racing is given by the following function, where no more than 100 wheels can 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 + 180x; (0,100]

The production would be 25 wheels,

Lowest average cost is $ 123.75

Step-by-step explanation:

Given cost function,

Where,

x = number of wheel,

So, the average cost per wheel,

Differentiating with respect to x,

Again differentiating with respect to x,

For maxima or minima,

For x = 25, A''(x) = positive,

i.e. A(x) is maximum at x = 25.

Hence, the production would be 25 wheels for the lowest average cost per wheel.

And, lowest average cost,

A(x) = 0.09(25)² - 4.5(25) + 180 = $ 123.75