Reference no: EM132688104

Management of the Albert Frank Co. has established goals for the market share it wants each of the company's two new products to capture in their respective markets.

Goal 1: Market share of product 1 is at least 15% Goal 2: Market share of product 2 is at least 10%

Three advertising campaigns are being planned to try to achieve these market shares. Campaign 1 is targets directly on the first product.

Campaign 2 targets the second product. Campaign 3 promotes both products.

Letting x1, x2, and x3 be the amount of money allocated (in millions of dollars) to these respective campaigns, the resulting market share (expressed as a percentage) for the two products are estimated to be

Market share for product 1 = 0.5%x1 + 0.2%x3

Market share for product 2 = 0.3%x2 + 0.2%x3

The two goals are equally weighted. Besides, a total of $55 million is available for the three advertising campaigns, but management wants at least $10 million devoted to the third campaign.

In this light, management wants to know how to most effectively allocate the available money to the three campaigns.

a. Formulate the goal programming model in mathematic form.

b. Solve the model formulated in part (a) on a spreadsheet, provide a screenshot of your model.

c. Interpret this solution to management in its language.

d. Look at the sensitivity report, if the penalty for not meeting product 1's market share goal is doubled from its current value, without resolving the model, can you tell whether the optimal production plan you obtained in part (b) will change? Why or why not? Explain.

e. Look at the sensitivity report, please explain the meaning of the shadow price associated with the constraint "A total of $55 million is available for the three advertising campaigns" in the problem context.