The Royal Seas Company runs a three-night cruise to the Caribbean from Port Canaveral. The company wants to run TV ads promoting its cruises to high-income men, high-income women, and retirees. The company has decided to consider airing ads during prime time, afternoon soap operas, and during the evening news. The number of exposures (in millions) expected to be generated by each type of ad in each of the company's target audiences is summarized in the following table: Prime Time Soap Operas Evening News High-income men 6 3 6 High-income women 3 4 4 Retirees 4 7 3 Ads during prime time, the afternoon soaps, and the news hour cost $120,000, $85,000, and $100,000, respectively. Royal Seas wants to achieve the following goals: Goal 1: Spend approximately $900,000 on TV advertising. Goal 2: Generate approximately 45 million exposures among high-income men. Goal 3: Generate approximately 65 million exposures among high-income women. Goal 4: Generate approximately 60 million exposures among retirees. (a) Formulate a GP model for this problem. Assume overachievement of the first goal is equally as undesirable as underachievement of the remaining goals on a percentage deviation basis. The company is indifferent on underachievement of the first goal and overachievement of the remaining goals. (Let X1, X2, and X3, be the number of prime time ads, ads during afternoon soap operas, and ads during the evening news that are purchased. Use CM and CP to denote the deviational variables c− and c+ associated with the goal involving cost. Use MM and MP to denote the deviational variables m− and m+ associated with the goal involving high-income men. Use WM and WP to denote the deviational variables w− and w+ associated with the goal involving high-income women. Use RM and RP to denote the deviational variables r− and r+ associated with the goal involving retirees. CM and CP are in thousands of dollars. MM, MP, WM, WP, RM, and RP are in millions of exposures. Use either 1 or 0 for all weights.) MIN: Subject to: costs (in thousands of dollars) exposures among high-income men (in millions) exposures among high-income women (in millions) exposures among retirees (in millions) X1, X2, X3, CM, CP, MM, MP, WM, WP, RM, RP ≥ 0 and integer

The Royal Seas Company runs a three-night cruise to the Caribbean from Port Canaveral. The company wants to run TV ads promoting its cruises to high-income men, high-income women, and retirees. The company has decided to consider airing ads during prime time, afternoon soap operas, and during the evening news. The number of exposures (in millions) expected to be generated by each type of ad in each of the company's target audiences is summarized in the following table: Prime Time Soap Operas Evening News High-income men 6 3 6 High-income women 3 4 4 Retirees 4 7 3 Ads during prime time, the afternoon soaps, and the news hour cost $120,000, $85,000, and $100,000, respectively. Royal Seas wants to achieve the following goals: Goal 1: Spend approximately $900,000 on TV advertising. Goal 2: Generate approximately 45 million exposures among high-income men. Goal 3: Generate approximately 65 million exposures among high-income women. Goal 4: Generate approximately 60 million exposures among retirees. (a) Formulate a GP model for this problem. Assume overachievement of the first goal is equally as undesirable as underachievement of the remaining goals on a percentage deviation basis. The company is indifferent on underachievement of the first goal and overachievement of the remaining goals. (Let X1, X2, and X3, be the number of prime time ads, ads during afternoon soap operas, and ads during the evening news that are purchased. Use CM and CP to denote the deviational variables c− and c+ associated with the goal involving cost. Use MM and MP to denote the deviational variables m− and m+ associated with the goal involving high-income men. Use WM and WP to denote the deviational variables w− and w+ associated with the goal involving high-income women. Use RM and RP to denote the deviational variables r− and r+ associated with the goal involving retirees. CM and CP are in thousands of dollars. MM, MP, WM, WP, RM, and RP are in millions of exposures. Use either 1 or 0 for all weights.) MIN: Subject to: costs (in thousands of dollars) exposures among high-income men (in millions) exposures among high-income women (in millions) exposures among retirees (in millions) X1, X2, X3, CM, CP, MM, MP, WM, WP, RM, RP ≥ 0 and integer

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Description: The Royal Seas Company runs a three-night cruise to the Caribbean from Port Canaveral. The company wants to run TV ads promoting its cruises to high-income men, high-income women, and retirees. The company has decided to consider airing ads during pr

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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	Prime Time	Soap Operas	Evening News
High-income men	6	3	6
High-income women	3	4	4
Retirees	4	7	3

Ads during prime time, the afternoon soaps, and the news hour cost $120,000, $85,000, and $100,000, respectively. Royal Seas wants to achieve the following goals:

Goal 1: Spend approximately $900,000 on TV advertising.
Goal 2: Generate approximately 45 million exposures among high-income men.
Goal 3: Generate approximately 65 million exposures among high-income women.
Goal 4: Generate approximately 60 million exposures among retirees.

(a)

Formulate a GP model for this problem. Assume overachievement of the first goal is equally as undesirable as underachievement of the remaining goals on a percentage deviation basis. The company is indifferent on underachievement of the first goal and overachievement of the remaining goals. (Let X₁, X₂, and X₃, be the number of prime time ads, ads during afternoon soap operas, and ads during the evening news that are purchased. Use CM and CP to denote the deviational variables

c⁻and c⁺associated with the goal involving cost. Use MM and MP to denote the deviational variables m⁻and m⁺

associated with the goal involving high-income men. Use WM and WP to denote the deviational variables w⁻and

w⁺associated with the goal involving high-income women. Use RM and RP to denote the deviational variables r⁻

and r⁺associated with the goal involving retirees. CM and CP are in thousands of dollars. MM, MP, WM, WP, RM, and RP are in millions of exposures. Use either 1 or 0 for all weights.)

MIN:

Subject to:

costs (in thousands of dollars)

exposures among high-income men (in millions)

exposures among high-income women (in millions)

exposures among retirees (in millions)

X₁, X₂, X₃, CM, CP, MM, MP, WM, WP, RM, RP ≥ 0 and integer

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