The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this years program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown:

Constraint Television Radio Newspaper

Audience per advertisement 100,000 18,000 40,000

Cost per advertisement $2000 $300 $600

Maximum media usage 10 20 10

To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. The promotional budget is limited to $18,200.

Westchester Chamber of Commerce wants to maximize total audience contact.

Using Excel Solver or OpenSolver , perform a sensitivity analysis and answer the questions below:

a) Identify the slack and/or surplus variable in each of the constraints.

b) specify the ranges in the objective function coefficients for which the current solution will remain optimal (ranges of optimality).

c) what are the shadow prices for each constraint? Interpret each.

d) specify the ranges in the right-hand side of each constraint for which the current shadow prices remain valid (ranges of feasibility).

e) Identify the reduced costs for each of the decision variables and interpret them