1) The marketing manager for Mountain Mist soda needs to decide how many TV spots and magazine ads to run during the next quarter. Each TV spot costs $5,000 and is expected to increase sales by 300,000 cans. Each magazine ad costs $2,000 and is expected to increase sales by 500,000 cans. A total of $100,000 may be spent on TV and magazine ads; however, Mountain Mist wants to spend no more than $70,000 on TV spots and no more than $50,000 on magazine ads. Mountain Mist earns a profit of $0.05 on each can it sells.
a) Formulate an LP model for this problem. Clearly label and define the decision variables, the objective function and each of the constraints.
b) Sketch the feasible region for this model using the graph paper available in Learn. What is the optimal solution?
2) Jim solved a linear program involving profit maximization, subject to various constraints, and obtained $120.2 as the optimal objective value. After solving the problem, he noticed that he forgot to include the most important constraint in his formulation. Then, he added that constraint and re-solved the problem. The new optimal objective value is $160.7. Do you trust in the new objective value Jim has come up with? Please explain your reasoning.