Marginal Profit

Question

Suppose that the marginal profit function for a company is P'(x)=120+34x-3x^2 at a production level of x units.

Find the extra profit earned from the sale of 6 additional units if 8 units have already been produced and sold.

Answer 1

P'(x) = 120+34x-3x^2 = marginal profit at output level = x

integrate

P(x) = 120x +17x^2 - x^3 + c = total profit at x output

P(8) = 120(8) +17(8)^2 - 8^3 + c = 960+17(64)- 512 =448+1088=1536+c

with 6 more, x=6+8=14 and

P(14) =120(14)+17(14^2)-14^3 +c = 2268 +c

increase in profit from x=8 to 14 is 2268-1536 = 732

c=the unknown constant likely= zero, but for this problem c does not change the result no matter what value it equals