a)The profit function for a certain commodity is given by𝑃(𝑥)=110𝑥−𝑥 2−1000. Find the level of production that yields maximum profit and hence find the maximum profit.

Question

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

2−1000. Find the

level of production that yields maximum profit and hence find the maximum profit.

Answer 1

Of course you could solve this with calculus by finding P'(x) and setting that to zero.

But if you realize that this is a parabola opening down, then the maximum can be found by

x = -b/2a = -110/(2(-1)) = 55.

Find the profit by P(55) = 2025.