Nov 2017 Q2

An advertising agency wishes to reach two types of audiences: Customers with annual income greater than GH¢ 15,000 (target audience A) and customers with annual income less than GH¢15,000 ( target audience B). The total advertising budget is GH¢ 200,000. One programme on TV advertising costs GH¢50,000; one programme on radio advertising costs GH¢20,000. For contract reasons, at least three programmes ought to be on TV, and the number of radio programmes must be limited to five. Surveys indicate that a single TV programme reaches 450,000 customers in target audience A and 50,000 in target audience B. One radio programme reaches 20,000 in target audience A and 80,000 in target audience B.
Required:
i) Formulate the linear programming problem.                                                                                                                  (4 marks)

ii) Construct the initial simplest tableau.                                                                                                                            (4 marks)

iii) Perform the first iteration.                                                                                                                                             (4 marks)

iv) Determine the media mix to maximize the total reach.                                                                                                 (4 marks)

v) Determine the shadow prices of the binding constraint.                                                                                                 (4 marks)