1. A toy manufacturer makes stuffed kittens and puppies that have relatively lifelike motions. There are three different mechanisms which can be installed in these "pets." These toys will sell for the same price regardless of the mechanism installed, but each mechanism has its own variable cost and setup cost. Profit, therefore, is dependent upon the choice of mechanism and upon the level of demand. The manufacturer has in hand a forecast of demand that suggests a 0.2 probability of light demand, a 0.45 probability of moderate demand, and a probability of 0.35 of heavy demand. Payoffs for each mechanism-demand combination appear in the table below.

a. Construct the appropriate decision tree to analyze this problem by using standard symbols for the tree (please be neat).

b. Analyze the decision tree and select the optimal decision for this manufacturer.

c. What is the EVPI for this manufacturer

2. Maxine's Hat Company produces three distinct hat styles. The operations manager has modeled the operations using linear programming. He is using x1, x2, and x3 to represent each hat style. Below is his formulation:

Maximize Z = 70 x1 + 80 x2 + 60 x3 Subject to:
Machine A: 2 x1 + 4 x2 + 2 x3 < 120 hours
Machine B: 5 x1 + 3 x2 + 2 x3 < 400 hours
Machine C: 2 x1 + 2 x2 + 4 x3 < 110 hours
x1 > 0; x2 > 0; x3 > 0

a. Use Excel and Solver to find the optimal solution for this problem. Provide printouts of worksheets for the final solution and the sensitivity report. Then consider the statements below independently, state whether they are true or false and explain each answer.

b. If the price of Hat 3 were to increase by $55, it would still remain to be part of the optimal product mix.

c. The capacity of Machine B can be reduce to 280 hours without affecting profits.

d. If machine C had a capacity of 115 hours, the production output would remain unchanged.