College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 1 - Equations and Inequalities - Exercise Set 1.7 - Page 198: 127

Answer

The company must be able to sell $more$ $than$ $1,200$ packages in order to make a profit.

Work Step by Step

To answer this exercise, we must first model the expense of production and the price of the packages sold: $$Expense = 3,000 + 3p$$ $$Price = 5.5p$$ where $p$ represents the amount of packages sold in a week. To make a profit, the company must be able to produce more money than their expenses, in other words: $$Price \gt Expense$$ $$5.5p \gt 3,000 + 3p$$ By solving for $p$: $$5.5p - 3p \gt 3,000$$ $$2.5p \gt 3,000$$ $$p \gt 1,200$$ which means that the company must be able to sell $more$ $than$ $1,200$ packages in order to make a profit.
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