Problem 1: Linear Programming [5 points]

An advertising agency is promoting a new perfume in the Baltimore market and wants to get the maximum exposure possible for it within a $100,000 advertising budget. To do so, the agency needs to decide how much of the budget to spend on each of two media outlets: (1) television spots during the late evening and (2) print ads in the Sunday edition of the Baltimore Sun. Each television spot costs $3,000; each Sunday newspaper ad costs $1,250. The expected exposure, based on ratings, is 35,000 viewers for each TV commercial and 20,000 readers for each newspaper advertisement. The agency director decides, based on experience with the Baltimore market, that at least 5 but no more than 25 television spots should be ordered, and that at least 10 newspaper ads should be contracted.

1. Present the LP formulation. Clearly identify the decision variables, objective function, and all constraints.

Decision variables: TV ad spots (x); newspaper ads (y)

Objective function: maximize exposure

E(x,y)=35,000x + 20,000y

Constraints: $100,000 budget; cost $3,000 per TV spot; $1,250 per print ad

$3,000x + $1,250y <= $100,000

Number of TV ads must be 5-25, so 5<=x<=25

Number of newspaper ads must 10+, so y>=10

1. Solve the problem using Excel Solver. How many TV spots and how many print ads should they purchase? What is the resulting exposure?

1. Attach the Sensitivity Reportas Exhibit A and the Answer Report as Exhibit B. Which constraints are binding?

1. Explain what the shadow price of a constraint is. What is the shadow price of the constraint that "at least 10 newspaper ads should be contracted?" What does this number tell us?

1. On the basis of your solution, is there any reason to be skeptical of the agency director's judgement that "at least 5 but no more than 25 television spots should be ordered?"