Example 6 Advertising Chapter 7.3 A business plans to use three methods of advertising: newspapers,...

example 6 Advertising

Chapter 7.3

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

a. Does AB or BA give the matrix that represents the cost of ads for each target group of people in each market?

b. Find this matrix.

c. For what group of people is the most money spent on advertising?

2009 PBLPathways

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

a. Does AB or BA give the matrix that represents the cost of ads for each target group of people in each market?

b. Find this matrix.

c. For what group of people is the most money spent on advertising?

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

a. Does AB or BA give the matrix that represents the cost of ads for each target group of people in each market?

12 10 3 12 15

10 8 5 16 10

5 9 10 11 6

AB

3 12 15 12 10

5 16 10 10 8

10 11 6 5 9

BA

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

a. Does AB or BA give the matrix that represents the cost of ads for each target group of people in each market?

12 10 3 12 15

10 8 5 16 10

5 9 10 11 6

AB

3 12 15 12 10

5 16 10 10 8

10 11 6 5 9

BA

(3 x 2)

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

a. Does AB or BA give the matrix that represents the cost of ads for each target group of people in each market?

12 10 3 12 15

10 8 5 16 10

5 9 10 11 6

AB

3 12 15 12 10

5 16 10 10 8

10 11 6 5 9

BA

(3 x 2) (3 x 3)

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

a. Does AB or BA give the matrix that represents the cost of ads for each target group of people in each market?

12 10 3 12 15

10 8 5 16 10

5 9 10 11 6

AB

3 12 15 12 10

5 16 10 10 8

10 11 6 5 9

BA

(3 x 2) (3 x 3)

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

a. Does AB or BA give the matrix that represents the cost of ads for each target group of people in each market?

12 10 3 12 15

10 8 5 16 10

5 9 10 11 6

AB

3 12 15 12 10

5 16 10 10 8

10 11 6 5 9

BA

(3 x 2) (3 x 3) (3 x 3) (3 x 2) (3 x 2)

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

a. Does AB or BA give the matrix that represents the cost of ads for each target group of people in each market?

12 10 3 12 15

10 8 5 16 10

5 9 10 11 6

AB

3 12 15 12 10

5 16 10 10 8

10 11 6 5 9

BA

(3 x 2) (3 x 3) (3 x 3) (3 x 2) (3 x 2)

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

b. Find this matrix.

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

b. Find this matrix.

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

b. Find this matrix.

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

b. Find this matrix.

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

5 12 16 10 10 5 270

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

b. Find this matrix.

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

5 12 16 10 10 5 270

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

b. Find this matrix.

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

10 10 11 8 6 9 242

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

b. Find this matrix.

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

c. For what group of people is the most money spent on advertising?

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

Mkt I Mkt II

Teens

Single females

Men 35-50

(3 x 3) (3 x 2)

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

c. For what group of people is the most money spent on advertising?

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

Mkt I Mkt II

Teens

Single females

Men 35-50

(3 x 3) (3 x 2)

Three target groups

(3 x 2)

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

c. For what group of people is the most money spent on advertising?

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

Mkt I Mkt II

Teens

Single females

Men 35-50

(3 x 3) (3 x 2)

Two markets

(3 x 2)

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

c. For what group of people is the most money spent on advertising?

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

Mkt I Mkt II

Teens

Single females

Men 35-50

2009 PBLPathways

A business plans to use three methods of advertising: newspapers, radio, and cable TV in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups, teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.

Mkt I Mkt II

Paper

Radio

TV

12 10

10 8

5 9

A

Paper Radio TV

Teens

Single females

Men 35-50

3 12 15

5 16 10

10 11 6

B

c. For what group of people is the most money spent on advertising?

3 12 15 12 10 231 261

5 16 10 10 8 270 268

10 11 6 5 9 260 242

BA

Mkt I Mkt II

Teens

Single females

Men 35-50