Question

The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model. P(x) = 230 + 40x - 0.5x2 What expenditure for advertising will yield a maximum profit?
A) 40
B) 0.5
C) 230
D) 20

Answer 1

Answer:

Option A

Step-by-step explanation:

Given that The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model.

$P(x) = 230 + 40x - 0.5x^2$

We can use derivative test to find maximum

Differentiate two times the profit funciton

$P'(x) = 40-x\\P"(x) = -1$

Equate I derivative to 0

we get

$x=40$

II derivative is alrways negative

Hence profit is maximum when x=40

Option A is right