# Advertising 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 believes 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. (b) Graph the region determined by these constraint inequalities.

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042
Chapter 4.1, Problem 31E
Textbook Problem
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## Advertising 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 believes 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.(b) Graph the region determined by these constraint inequalities.

(a)

To determine

The system of inequalities which describes the constraints on the number of each type of 1–minute spots required to reach the target groups.

### Explanation of Solution

Given Information:

In an advertising campaign to target the most likely customers, Apex Motors which manufacturers luxury cars and sports-utility vehicles plans to run 1–minute spots on business/investment program through which 7 million women and 4 million men can be grasped and also they planned 1–minute spots on sports events, through which 2 million women and 12 million men can be grasped. The target of the company is to grasp at least 30 million women and 28 million men who are prospective customers.

Explanation:

Consider the provided information,

First define the variables. The experiment involves two types of advertisements, finance programs and sports programs. So, define

x=number of minutes on finance programs And y=the number of minutes on sports programs.

The two constraints provided in the problem are the target that the ads much grasp at least 30 million women and 28 million men who are prospective customers

(b)

To determine

To graph: The region that describes the constraints on the number of each type of 1-minute spots required to reach the target groups.

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