Question

A manufacturer of a product has a monthly cost for producing x items given by C(x) = 10+2x. The selling price function for this product is p(x) = 50-.01x. Find the maximum profit the company can expect monthly

Answer 1

the revenue function is price * quantity, so
R(x) = x(50-.01x)
profit is revenue less cost, so

P(x) = R(x)-C(x)
= x(50-.01x) - (10+2x)
= -0.01x^2 + 48x - 10

Now just set dP/dx=0 and evaluate P there.

Or, just use your Algebra I skills and find the vertex of the parabola.

Answer 2

profit = p(x) - C(x)
= 50-.01 x - 10 - 2x
= 40-2.01 x
max at x = 0
I bet you have a typo though.

Answer 3

Oh, go with what Steve said.