Advertising Optimization a. The Lakeview Recreational Center provides a variety of tness services (racquetball courts, gymnasium, treadmills, exercise bicycles, and so forth). It wants to optimize its use of weekday 30-second commercials on a local radio station. Lakeview officials have identified five 3-hour time periods in which it could place its advertisements (the "AM Drive" from 6:00 - 9:00 a.m., an "AM talk show" from 9:00 am. - 12:00 noon, a "PM talk show" from 12:00 - 3:00 p.m., the "PM Drive" from 3:00 - 6:00 p.m., and a "PM Music" period from 6:00 - 9:00 pm}. Commercials in each time period incur different costs, with advertisements during the "AM Drive" period being the most expensive. Lakeview's radio advertising budget is $750. Furthermore, Lakeview has selected five consumer segments their radio advertisements could reach (teenagers, men age 20- 39, men age 40 and above, women age 20-39, and women age 40 and above). Each radio commercial time period option reaches a different exposure of the consumer segments. Company officials have established minimum exposure targets for each of these segments. Formulate and solve a linear programming model, using the data as provided in Adept- Shell.xls, to determine the advertising strategy that maximizes the number of "excess radio exposures" (those exposures over and above the minimum requirements), while staying within budgetary restrictions. Name your sheet Model1. b. After solving the model, do you nd that you get integer or fractional values for some or all of the decision variables? c. Create a copy of your original model sheet and work this copy for this part of the problem. Name this sheet, Model2. Modify the model to ensure you get an all integer solution? What happens to your solution and the overall objective function value if you only allow integer solutions? d. Create another copy of your original model sheet and work with this copy for this part of the problem Name this sheet, Models. In looking at the excess exposures in your solution, you may nd that the number of excess exposures varies widely by market segment. How might you modify this model to try to get it to suggest a solution that results in excess exposures that are more "evenly distributed " across the market segments? Note that there are multiple ways you might do this and you'll have to be a bit clever. Build the revised model to attempt to do this - make sure you still get integer solutions. Make sure you describe, in a cell comment, your model modifications and the thinking that went behind it. Solve the new model and discuss the results. Is your new model still linear - why or why not? Does your new model appear "harder to solve"? Does the solution change from the previous versions of the model
