Apex Motors manufactures luxury cars and sport utility vehicles. The most likely

Question

Apex Motors manufactures luxury cars and sport utility vehicles. The most likely customers are high-income men and women, and company managers want to initiate an advertising campaign targeting these groups. They plan to run 1-minute spots on business/investment programs, where they can reach 7 million women and 4 million men from their target groups. They also plan 1-minute spots during sporting events, where they can reach 2 million women and 12 million men from their target groups. Apex feels that the ads must reach at least 30 million women and at least 28 million men who are prospective customers.

(a) Write the inequalities that describe the constraints on the number of each type of 1-minute spots needed to reach these target groups. (Let x represent minutes of business/investment program ads, and let y represent minutes of sporting events ads.)

Explanation / Answer

(a). Let Apex Motors run x -minutes of advertisements on business/investment programs and y minutes of advertisements during sporting events. Then Apex Motors can reach 7x+2y million women and 4x+12y million men.

Thus, 7x+2y ? 30 and 4x+12y ? 28.

constraint on millions of women reached

constraint on millions of men reached

No. of minutes of advertisements run on business/investment programs

x

7x

4x

No. of minutes of advertisements run during sporting events

y

2y

12y

constraint on millions of women reached

constraint on millions of men reached

No. of minutes of advertisements run on business/investment programs

x

7x

4x

No. of minutes of advertisements run during sporting events

y

2y

12y

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