Find level of production yielding maximum profit hence find maximum profit

Question

.

a)The profit function for a certain commodity is given by 𝑃 (𝑥)=110𝑥−𝑥

2−1000. Find the The level of production that yields maximum profit and hence find the maximum profit

(6 marks)

Answer 1

P = 110x -x^2 -1000

take the derivative and set equal to zero

P' = 110-2x = 0

x =110/2 = 55 = profit maximizing out put level

P(55) = 110(55) -55^2 -1000 = 6050-3025-1000= 2025 = maximum profit