Part A: The manager of Canadian Tire is attempting to decide on the types and amounts of advertising the store should use. She has invited representatives from the local radio station, television station and newspaper to make presentations in which they describe their audiences. The television station representative indicates that a TV commercial, which costs $15,000 would reach 25,000 potential customers. The breakdown of the audience is as follows: Male Female Senior 5000 5000 Youth 5000 10000 The newspaper representative claims to be able to provide an audience of 10,000 potential customers at a cost of $4,000 per ad. The breakdown of the audience is as follows: Male Female Senior 4000 3000 Youth 2000 1000 The radio station representative says that the audience for one of the stations commercials, which costs $6,000, is 15,000 customers. The breakdown of the audience is as follows: Male Female Senior 1500 1500 Youth 4500 7500 The store has the following advertising policy: Use at least twice as many radio commercials as newspaper ads Reach at least 100,000 customers Reach at least twice as many youth as seniors Make sure that at least 30% of the audience is female Available space limits the number of newspaper ads to 7. The store wants to know the optimal number of each type of advertising to purchase to minimize total cost. Formulate a linear programming model for this problem and solve it in Excel. NOTE: as we have done in class, accept fractional answers (DO NOT require your answer to be integer) Q1. How many constraints are there in your formulation (not including non-negativity)?

Q2. What percentage of the audience is female in the optimal solution? Q3. How many TV ads are purchased in the optimal solution? Q4. How many constraints are binding in the optimal solution? Q5. How does the number of youth reached compare to the number of senior citizens reached? Part B: Suppose a second radio station approaches the department store and indicates that its commercials, which cost $7,500 each, reach 18,000 customers with the following demographic breakdown: Male Female Senior 2400 3600 Youth 4000 8000 If the store were to consider this station along with the other media alternatives, how would this affect the solution? Q6. How many variables are there in this model? Q7. Which radio stations are ads purchased from? Q8. What happens to the total cost?