P=245−x50 and C(x)=46000+60x, x is the number of microwaves that can be sold at a price of p dollars and C(x) is the cost of production

Question

1. Find the profit function in terms of x. P(x) =
2. Evaluate the marginal profit function at x=1500. P′(1500) =

Answer 1

Profit = Revenue - Cost = R-C = Px - C = 245x-50x^2 - 46000-60x = -50x^2+185x-46,000

Marginal profit is the derivative of the profit function

Marginal profit = -100x + 185

for x=1500, Marginal profit = -100(1500) +185 = -150000 + 185 = 149815