Chapter 10.GA, Problem 1GA

Business Analysis

This activity may be completed by working in groups or individually.

Suppose you own a small business that manufactures specialized iPod covers. You need to decide how many covers to make. The more covers you make, the lower the price you will have to charge to sell them all. Naturally, each cover you make cost you because you must buy the materials to make each cover. The following table summarizes some factors you must consider in deciding how many covers to make, along with algebraic representations of those factors.

Number of covers	Description	Algebraic Expression
Total manufacturing expenses	This is total amount that it will cost to manufacture all the iPod covers. It will cost $100 to buy special equipment to manufacture the covers in addition to materials costing $0.50 per cover.	$100+0.50x$
Price charged per cover	For additional cover produced, the price that must be charged per cover decreases from $40 by an additional $0.50.	$40-0.05x$

Revenue is the amount of money collected from the selling the iPod covers. Revenue can be found by multiplying the price charged per cover by the number of covers sold. Use the algebraic expressions given in the table above to find a polynomial that represents the revenue from sales of covers. Then write this polynomial in the Polynomial column next to “Revenue” in the table to the right.

			Number of Covers, $x$
	Polynomial	200	300	400	500	600
Revenue
Total manufacturing expenses	$100+0.50x$
Profit	$$