Question

The profit function for a certain commodity is

P(x) = 120x − x² − 2000.

Find the level of production that yields maximum profit, and find the maximum profit.

Answer 1

Given profit function: P (x) = 120x - x^2 - 2000

For maximium profit, we will differentiate the given profit function as per below:

dP /dx = 120 - 2x

At maximum profit, dP / dx = 0, so,

120 - 2x = 0

-2x = -120

x = 120 / 2 = 60

So, level of production that yields maximum profit is 60.

now, we will put the value of x in the profit function to calculate the value of maximum profit as below:

P (x) = 120 * (60) - (60)^2 - 2000

P (x) = 7200 - 3600 - 2000

P (x) = 1600

So, maximum profit is 1600.