poblem about math

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 = 230 + 50x − 0.5x².

 What expenditure for advertising yields a maximum profit?

Answer 1

P= 230+50x-.5x^2

P'=50-x=0

x=50

=50 times $500

=$5,000

P=230+50(50)-.5(50)^2

=230+1250

=1480

=1480 times $500

=$148,000=maximum profit