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:

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:

The radio station representative says that the audience for one of the station's commercials, which costs

$$6,000,$ is $15,000$ customers. The breakdown of the audience is as follows:

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$)$

Q$1.$ How many constraints are there in your formulation $($not including non$-$negativity$)?$Q$2.$ What percentage of the audience is female in the optimal solution?

Q$3.$ How many TV ads are purchased in the optimal solution?

Q$4.$ How many constraints are binding in the optimal solution?

Q$5.$ 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:

If the store were to consider this station along with the other media alternatives, how would this affect

the solution?

Q$6.$ How many variables are there in this model?

Q$7.$ Which radio stations are ads purchased from?

Q$8.$ What happens to the total cost?