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 shown below.

P = 190 + 80x – 0.5x^2
What expenditure for advertising will yield a maximum profit?

Answer 1

The profit:
P = - 0.5 x² + 80 x + 190
The maximum profit will be at the vertex :
x = - b / 2 a = - 80 : ( 2 * ( - 0.5 )) = - 80 : ( - 1 ) = 80 ( in hundreds of dollars )
Answer:
The amount of money that will yield a maximum profit is $8,000.