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An advertising firm desires to reach two types of audiences-customers with annual income of more than K40,000 (target audience A) and customers with annual income of less than K40,000 (target audience B). The total advertising budget is K200, 000 . One programme of TV advertising costs K50, 000 while one programme of radio advertising cost K20, 000. Contract conditions ordinarily require that there should be at least 3 programmes on TV and not more than 5 on radio. Survey indicates that one TV programme reaches 750,000 customers in target audience A and 150,000 in target audience B. One radio programme reaches 400,000 customers in target audience A and 260,000 in target audience B. Formulate a linear programming model for this problem Use the simplex method to determine the media mix to maximize the number of customers reached.

An advertising firm desires to reach two types of audiences-customers with annual income of more than K40,000 (target audience A) and customers with annual income of less than K40,000 (target audience B). The total advertising budget is K200, 000 . One programme of TV advertising costs K50, 000 while one programme of radio advertising cost K20, 000. Contract conditions ordinarily require that there should be at least 3 programmes on TV and not more than 5 on radio. Survey indicates that one TV programme reaches 750,000 customers in target audience A and 150,000 in target audience B. One radio programme reaches 400,000 customers in target audience A and 260,000 in target audience B. Formulate a linear programming model for this problem Use the simplex method to determine the media mix to maximize the number of customers reached.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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An advertising firm desires to reach two types of audiences-customers with annual income of more than K40,000 (target audience A) and customers with annual income of less than K40,000 (target audience B). The total advertising budget is K200, 000 . One programme of TV advertising costs K50, 000 while one programme of radio advertising cost K20, 000. Contract conditions ordinarily require that there should be at least 3 programmes on TV and not more than 5 on radio. Survey indicates that one TV programme reaches 750,000 customers in target audience A and 150,000 in target audience B. One radio programme reaches 400,000 customers in target audience A and 260,000 in target audience B.

  1. Formulate a linear programming model for this problem
  2. Use the simplex method to determine the media mix to maximize the number of customers reached.
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