Question

Consider this Revenue Advertising Expense situation.

A drugstore that sells a certain brand of vitamin capsule estimates that
the profit P (in pesos) is given by P = −50x³ + 2400x² − 2000, 0 ≤ x ≤ 32 where x is the amount spent on advertising (in thousands of pesos). An
advertising agency provides four (4) different advertising packages with

costs listed below.

Which of these packages will yield the highest revenue
for the company?

A. Package A: Php 8,000.00

B. Package B: Php 16,000.00

C. Package C: Php 32,000.00

D. Package D: Php 48,000.00 ​

Answer 1

Package C: Php 32,000.00

Explanation:

Answer 2

• C. Package C: Php 32,000.00

Explanation:

Given function

• P = −50x³ + 2400x² − 2000, 0 ≤ x ≤ 32

x is the amount spent on advertising (in thousands of pesos).

Substitute x with 8, 16 and 32 and solve for P.

The greatest value of P is at:

• x = 32 ( Php 32000.00)

and the value is

• P = 817200.00

Another method is graphing.

See the attached picture for graphical solution.