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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