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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. Cost per Audience Reached per Advertisement Advertisement Maximum Numer of Advertisement Category TV Radio Internet Priority Level 2 Goal s.t. Priority Level 3 Goal Min P, 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 1: Reach at least 3.7 million people. Priority Level 4 Goal 200,000 50,000 100,000 $2,500 $400 $500 Goal 2: The number of television advertisements should be at least 30% of the total number of advertisements. TV limit X₁ ≤ 10 10 Goal 3: The number of radio advertisements should not exceed 20% of the total number of advertisements. x 15 Goal 4: Limit the total amount spent for advertising to $20,000. (a) Formulate a goal programming model for this problem. (Let x, number of TV advertisements, x₂= number of radio advertisements, x, number of internet advertisements, let dp be the deviation variable which is greater than the value of goal, and let do, be the deviation variable which is less than the value of goal i, for/= 1, 2, 3, 4.) + P₂ 18 X x +PA X

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. Cost per Audience Reached per Advertisement Advertisement Maximum Numer of Advertisement Category TV Radio Internet Priority Level 2 Goal s.t. Priority Level 3 Goal Min P, 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 1: Reach at least 3.7 million people. Priority Level 4 Goal 200,000 50,000 100,000 $2,500 $400 $500 Goal 2: The number of television advertisements should be at least 30% of the total number of advertisements. TV limit X₁ ≤ 10 10 Goal 3: The number of radio advertisements should not exceed 20% of the total number of advertisements. x 15 Goal 4: Limit the total amount spent for advertising to $20,000. (a) Formulate a goal programming model for this problem. (Let x, number of TV advertisements, x₂= number of radio advertisements, x, number of internet advertisements, let dp be the deviation variable which is greater than the value of goal, and let do, be the deviation variable which is less than the value of goal i, for/= 1, 2, 3, 4.) + P₂ 18 X x +PA X

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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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. Cost per Audience Reached per Advertisement Advertisement Category TV Radio Internet s.t. Priority Level 2 Goal Priority Level 3 Goal Goal 1: Reach at least 3.7 million people. Priority Level Goal TV limit X₁ <10 Radio limit X₂ ≤ 15 Internet limit X3 ≤18 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 1 200,000 Goal 2 50,000 Goal 3 100,000 X Goal 2: The number of television advertisements should be at least 30% of the total number of advertisements. ✓ $2,500 X $400 Goal 3: The number of radio advertisements should not exceed 20% of the total number of advertisements. $500 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 d; be the deviation variable which is less than the value of goal i, for i = 1, 2, 3, 4.) Min P. Maximum Numer of Advertisement 10 15 x 18 + P3 X (!) + P4 x
Transcribed Image Text: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. Cost per Audience Reached per Advertisement Advertisement Category TV Radio Internet s.t. Priority Level 2 Goal Priority Level 3 Goal Goal 1: Reach at least 3.7 million people. Priority Level Goal TV limit X₁ <10 Radio limit X₂ ≤ 15 Internet limit X3 ≤18 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 1 200,000 Goal 2 50,000 Goal 3 100,000 X Goal 2: The number of television advertisements should be at least 30% of the total number of advertisements. ✓ $2,500 X $400 Goal 3: The number of radio advertisements should not exceed 20% of the total number of advertisements. $500 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 d; be the deviation variable which is less than the value of goal i, for i = 1, 2, 3, 4.) Min P. Maximum Numer of Advertisement 10 15 x 18 + P3 X (!) + P4 x
Goal 4 X₁ dpj nj≥ 0 for / = 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.) Category TV Radio X Check the plus and minus signs of all terms and/or values. Internet Number of Advertisements
Transcribed Image Text:Goal 4 X₁ dpj nj≥ 0 for / = 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.) Category TV Radio X Check the plus and minus signs of all terms and/or values. Internet Number of Advertisements
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