Question

The revenue from a company’s factory in Scranton, PA is given by 2n2-15n+23, where n represents the number of paper goods produced in the factory. The cost in dollars of producing paper goods is given by n2+3n+23. Write and simplify a polynomial expression for the profit from making and selling n paper goods.

Answer 1

The polynomial expression for the profit from making and selling 'n' paper goods, is;

n × (n - 18)

Explanation:

The revenue, 'R', and the cost, 'C', from the company's Scranton, PA factory are as follows;

R = 2·n² - 15·n + 23

C = n² + 3·n + 23

The profit, 'P', is the revenue, 'R', in excess of the cost, 'C', therefore;

The profit, P = R - C

By substituting the polynomials representing 'R', and 'C', we have;

P = 2·n² - 15·n + 23 - (n² + 3·n + 23)

∴ P = 2·n² - n² - 15·n - 3·n + 23 - 23

P = n² - 18·n = n·(n - 18)

P = n·(n - 18)

The polynomial expression for the profit from making and selling 'n' paper goods, is P = n·(n - 18).