Suppose r(x) = 8(x)^(1/2) represents revenue and c(x) = 2(x)^2 represents cost, with x measured in thousands of units. Is there a production level that maximizes profit? If so, what is it?

Answer 1

profit = revenue - cost
= 8√x - 2x^2

d(profit)/dx = 4/√x - 4x
= 0 for a max of profit

4/√x = 4x
x = 1

since x was measured in thousands,
they should have a production of 1000