Your local Chamber of Commerce periodically sponsors public service seminars. In your role as the marketing manager, you are putting together an advertising plan for this year's program of events. The promotional budget is $25,000. Advertising alternatives include television, radio and newspaper. You have obtained the following estimates for the size of an audience and cost for each type of advertisement:

Past experience suggests that at most ten TV advertisements should be aired. Similarly, no more than 15 newspaper ads will be placed. For radio, maximum usage is set at 15 advertisements. You must find the mix of advertisements that will reach a maximum audience. You have decided to use linear programming to obtain a solution to the problem before you.

Give the full mathematical model for this problem.

1. What are the decision variables for this problem?
2. Using decision variables identified in part (a), formulate the objective function for this problem. Is the quantity of interest to be maximized or minimized? Explain briefly.
3. What is the limited resource in this problem? Using decision variables from part (a), formulate the constraint for this resource.
4. What other constraints are relevant to this problem? Using the decision variables from part (a), formulate those constraints.
5. Suppose that to ensure a balanced use of advertising media, radio advertisements must not exceed 60% of the total number of advertisements authorized. Using decision variables from part (a), formulate a constraint based on this requirement. Use algebra to rewrite this constraint in the standard linear format.
6. Suppose that, in addition, television should account for at least 5 % of the total number of advertisements authorized. Using decision variables from part (a), formulate a constraint based on this requirement in the standard linear format.  

Use SOLVER to produce the answer and sensitivity reports required to answer the following questions.

1. What is the optimal number of adverts for each of the media?

2. What is the maximum audience?

3. How much of the budget has been spent?

4. If the radio audience per advertisement doubled to 36,000 would the optimum number of advertisements change? Explain how you know.

5. If the provisional budget is increased to $30,000 what impact, if any, will this increase have on the maximum audience?

Question 2:

In January 2002, John, having recently graduated from UNISA established a business as a financial advisor. His uncle who was planning to retire in one years time asked John to recommend a management investment fund that he can investment in by buying units on a weekly basis. The uncle also wanted the option to sell his units at any time at the current price. John's uncle recently complained to John that he had received very poor advice and that he was not in a position financially to retire as he had planned. Thinking back to his QMB course John decided to summarize the weekly prices data for about the past two and a half years.  The data file is available on the portal  (Assignment 2  Future Leaders.xls)

 John asks you to summarize the data

(a) Make a histogram and obtain Descriptive Statistics, including Quartile 1 and Quartile 3 for both data sets, . Attach printouts of your data, histogram and Descriptive Statistics to your assignment submission.