Question

The advertising alternatives tor a company include television, radio, and newspaper ad- vertisements. The costs and estimates for audience coverage are given in table below: Television Newspaper Radio 2,000 Cost per advert Audience per advert 600 300 100, 000 40, 000 18,000 The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is €18.200. The company want to maximise the total audience. 1. Express this maximisation problem in its standard form - i.e., formulate the equa tions that describe the linear programming problem outlined above (note: there are four constraints) 15 marks 2. Using 3 iterations of the simplex method to show that the optimal solution is: Basic 22 T3 S 2 3 Sol'n 0 1,052,000 118,000 272.000 60,000 2 0 0 0 T1 0 0 23 23 23 T2 0 1 0 0 10 20 0 14 12 S4 0 0 0 23 where ri, 32 and r3 represent the number of advertisements in television, newspaper and radio, respectively 20 marks 3. How do you know that the solution in Q2. is optimal? 2 marks] 4. How many advertisements should be run in each of the three types of media to maximise the total audience? 3 marks] 5. The company realise that in their initial analysis, they forgot to allow for the ad- ministration cost per advert - i.e., 100, 50 and 20 per advert for television, newspaper and radio, respectively. The weekly administration budget is 1,200 (a) Using the optimal solution from Q2., set up the new augmented matrix and state the row operations required (do not perform the row operations) that would return the solution to its optimal form 8 marks (b) Without performing row operations, will the additional constraint change how many advertisements should be run in each of the three types of media to maximise the total audience? Justify your answer [2 marks]

Answer 1

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