The marginal profit function for x barbeque is P'(x) = 52 - 0.8x, find the average marginal profit from the first 40 grills produced and sold.

Question

This is for my calculus class and, while I usually use youtube for things I dont understand, I cannot figure this one out

Answer 1

P'(x)=52-0.8x is the marginal profit function.

The average marginal profit is P'(x)/x per unit. This is not the same as the average profit per unit.

So when x=40, P'(40)/40=(52-32)/40=20/40=0.5 per unit (barbecue).

However, the average is 35.6 based on summing P'(x) for x between 1 and 40 and dividing the result by 40. 

The average can also be calculated:

∫[0,40](52-0.8x)dx=[52x-0.4x²]|⁴⁰₀=1440, then divide by 40=36.