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 23 million women and at least 24 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.)

B)Graph the region determined by these constraint inequalities.

Answer 1

a)

x is the number of minutes of business/investment program commercials and y is the number of minutes of sporting events commercials

x,y >= 0

Since,in 1 minute spots on business/investment programs,they can reach 7 million women and in 1 minute spots during sporting events,they can reach 2 million women and the ads must reach at least 30 million women thus

Similarly for men:

System of inequalities:

b)

Shaded region is considered