Question

Suppose that the profit (in dollars) for a company when x units of product are produced is given by P(x)=(100−x)ln(x) for x>1. When the current production level is x=28 units, then the profit is

Answer 1

The profit when the current production level is 28 units is approximately $239.71.

Step-by-step explanation:

The profit for a company when x units of product are produced is given by the function P(x) = (100 - x)ln(x). To find the profit when the current production level is x = 28 units, we substitute x = 28 into the function:

P(28) = (100 - 28)ln(28)

P(28) = 72ln(28)

Using a calculator, we can approximate this as:

P(28) ≈ 72(3.33220451)

P(28) ≈ 239.7099132

Therefore, when the current production level is 28 units, the profit is approximately $239.71.