Problem #1 (52 points) Suppose you are hired by the Ohio Environmental Protection Agency as the publicity coordinator. A series of information seminars and workshops are being planned and it is your responsibility to put in place an advertising program, at the minimum cost, that will reach at least 1,000,000 people. You can choose either television, radio, or both as the means of advertising. The estimated audience reached, advertisement costs and maximum medium use (i.e., the limit placed on the use of each medium by communications regulatory agencies) figures for each of the television or radio session are in the following table: Television Radio Potential audience reached per advertisement session 100,000 25,000 Cost per advertisement session $2,000 $750 Maximum media use limitations*** 20 16 * No more than 20 and 16 television and radio sessions may be used respectively. ** To ensure a balanced coverage you are to have no more than 50 percent of the total advertisement sessions devoted to radio. 1.1 1.2 1.3 1.4 1.5 Express this information as a linear programming problem. There should be four structural constraints. (10 points) Solve this problem using computer and summarize the optimal solution you found. What factors are "limiting" in the solution? Also save and print out your answer report and sensitivity report for further use (you are not required to use them here in 1.2). (8 points) What if you are required to have AT LEAST 50 percent of the total advertisement spots devoted to radio? What factors are limiting the solution in this situation? (8 points) Similar to 1.3, if radio spots are required to be NO MORE than 30 percent of the total advertisement spots, what would be your solution? Modify your computer set ups in 1.2 to see the results and briefly interpret your solution. (8 points) Now suppose that you have an opportunity to put the radio advertisements on a different radio station. While the potential audience reached per radio session would not change, the station is willing to do the radio ads at a cost of $300 per session. Use your sensitivity report generated in 1.2 (attach with your assignment) to see whether this changes your answer for 1.2? If not, why not? If so, how would the answer change? (10 points) Go back to the original version and solution for the problem (i.e., those in question 1.1). Now suppose that the communications regulatory agency changes the rules regarding media use limitations so that there are no limits for either television or radio ads (i.e., the requirements in * and ** are removed). Would this change your answer for 1.2? If not, why not? If so, how would the answer change? (8 points) 1.6 Problem #1 (52 points) Suppose you are hired by the Ohio Environmental Protection Agency as the publicity coordinator. A series of information seminars and workshops are being planned and it is your responsibility to put in place an advertising program, at the minimum cost, that will reach at least 1,000,000 people. You can choose either television, radio, or both as the means of advertising. The estimated audience reached, advertisement costs and maximum medium use (i.e., the limit placed on the use of each medium by communications regulatory agencies) figures for each of the television or radio session are in the following table: Television Radio Potential audience reached per advertisement session 100,000 25,000 Cost per advertisement session $2,000 $750 Maximum media use limitations*** 20 16 * No more than 20 and 16 television and radio sessions may be used respectively. ** To ensure a balanced coverage you are to have no more than 50 percent of the total advertisement sessions devoted to radio. 1.1 1.2 1.3 1.4 1.5 Express this information as a linear programming problem. There should be four structural constraints. (10 points) Solve this problem using computer and summarize the optimal solution you found. What factors are "limiting" in the solution? Also save and print out your answer report and sensitivity report for further use (you are not required to use them here in 1.2). (8 points) What if you are required to have AT LEAST 50 percent of the total advertisement spots devoted to radio? What factors are limiting the solution in this situation? (8 points) Similar to 1.3, if radio spots are required to be NO MORE than 30 percent of the total advertisement spots, what would be your solution? Modify your computer set ups in 1.2 to see the results and briefly interpret your solution. (8 points) Now suppose that you have an opportunity to put the radio advertisements on a different radio station. While the potential audience reached per radio session would not change, the station is willing to do the radio ads at a cost of $300 per session. Use your sensitivity report generated in 1.2 (attach with your assignment) to see whether this changes your answer for 1.2? If not, why not? If so, how would the answer change? (10 points) Go back to the original version and solution for the problem (i.e., those in question 1.1). Now suppose that the communications regulatory agency changes the rules regarding media use limitations so that there are no limits for either television or radio ads (i.e., the requirements in * and ** are removed). Would this change your answer for 1.2? If not, why not? If so, how would the answer change? (8 points) 1.6
