7 A committee in charge of promoting a Ladies Professional Golf Association tournament is trying to determine how best to advertise the event during the two weeks prior to the tournament. The committee obtained the following information about the three advertising media they are considering using. Category Min P. s.t. TV Radio Internet TV limit Radio limit Goal 1: Reach at least 3.7 million people. Internet limit Goal 1 Goal 2 Goal 3 Goal 4 TV Audience Reached per Advertisement The last column in this table shows the maximum number of advertisements that can be run during the next two weeks; these values should be treated as constraints. The committee established the following goals for the campaign. Priority Level 1 Goal Category Radio 200,000 Priority Level 2 Goal Goal 2: The number of television advertisements should be at least 30% of the total number of advertisements. Priority Level 3 Goal Goal 3: The number of radio advertisements should not exceed 20% of the total number of advertisements. Priority Level 4 Goal Goal 4: Limit the total amount spent for advertising to $20,000. (a) Formulate a goal programming model for this problem. (Let x₁ = number of TV advertisements, x₂ = number of radio advertisements, x3 = number of internet advertisements, let dpi be the deviation variable which is greater than the value of goal i, and let dni be the deviation variable which is less than the value of goal i, for i=1, 2, 3, 4.) 50,000 Internet 100,000 P₂ Cost per Advertisement $2,500 $400 $500 Maximum Numer of Advertisement + P3 10 15 18 X dj dnj 20 for i = 1, 2, 3, and j = 1, 2, 3, 4 (b) Use the goal programming computer procedure to solve the model formulated in part (a). (Round your answers down to the nearest integer.) Number of Advertisements ]) + P₂([ PA
7 A committee in charge of promoting a Ladies Professional Golf Association tournament is trying to determine how best to advertise the event during the two weeks prior to the tournament. The committee obtained the following information about the three advertising media they are considering using. Category Min P. s.t. TV Radio Internet TV limit Radio limit Goal 1: Reach at least 3.7 million people. Internet limit Goal 1 Goal 2 Goal 3 Goal 4 TV Audience Reached per Advertisement The last column in this table shows the maximum number of advertisements that can be run during the next two weeks; these values should be treated as constraints. The committee established the following goals for the campaign. Priority Level 1 Goal Category Radio 200,000 Priority Level 2 Goal Goal 2: The number of television advertisements should be at least 30% of the total number of advertisements. Priority Level 3 Goal Goal 3: The number of radio advertisements should not exceed 20% of the total number of advertisements. Priority Level 4 Goal Goal 4: Limit the total amount spent for advertising to $20,000. (a) Formulate a goal programming model for this problem. (Let x₁ = number of TV advertisements, x₂ = number of radio advertisements, x3 = number of internet advertisements, let dpi be the deviation variable which is greater than the value of goal i, and let dni be the deviation variable which is less than the value of goal i, for i=1, 2, 3, 4.) 50,000 Internet 100,000 P₂ Cost per Advertisement $2,500 $400 $500 Maximum Numer of Advertisement + P3 10 15 18 X dj dnj 20 for i = 1, 2, 3, and j = 1, 2, 3, 4 (b) Use the goal programming computer procedure to solve the model formulated in part (a). (Round your answers down to the nearest integer.) Number of Advertisements ]) + P₂([ PA
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:7
A committee in charge of promoting a Ladies Professional Golf Association tournament is trying to determine how best to advertise the event during the two weeks prior to
the tournament. The committee obtained the following information about the three advertising media they are considering using.
Category
Min P.
TV
Radio
Internet
s.t.
Priority Level 4 Goal
Goal 1: Reach at least 3.7 million people.
TV limit
Radio limit
Internet limit
Goal 1
Goal 2
The last column in this table shows the maximum number of advertisements that can be run during the next two weeks; these values should be treated as constraints. The
committee established the following goals for the campaign.
Priority Level 1 Goal
Goal 3
Goal 4
Audience Reached
per Advertisement
Priority Level 2 Goal
Goal 2: The number of television advertisements should be at least 30% of the total number of advertisements.
Priority Level 3 Goal
Goal 3: The number of radio advertisements should not exceed 20% of the total number of advertisements.
TV
Category
200,000
50,000
Goal 4: Limit the total amount spent for advertising to $20,000.
(a) Formulate a goal programming model for this problem. (Let x₁ = number of TV advertisements, x₂ = number of radio advertisements, x3 = number of internet
advertisements, let do; be the deviation variable which is greater than the value of goal i, and let dni be the deviation variable which is less than the value of goal i,
for i=1, 2, 3, 4.)
Radio
100,000
Cost per
Advertisement
Internet
$2,500
Number of
Advertisements
$400
$500
Maximum Numer of
Advertisement
10
15
X₁ dpj dnj≥0 for i = 1, 2, 3, and j = 1, 2, 3, 4
(b) Use the goal programming computer procedure to solve the model formulated in part (a). (Round your answers down to the nearest integer.)
18
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