A company is concerned about the amount of usable components it receives from a supplier. For a set up cost of $800 and a variable cost of $60 the company can make their own parts. The company can buy reconditioned components in batches from a supplier but the number of usable components varies significantly. These reconditioned parts come in batches of 50 and the company has recently been paying $2200 for these batches. Furthermore, the supplier will provide fully tested and guaranteed components for $100 each. The company needs 45 components to fulfill a new contract.

For the reconditioned parts, the operations manager estimates that:

(a) half the time that at least 85% of the components in a batch will be usable;

(b) at most 98% of the components will be usable;

(c) there will be at least 75% of the components will be usable;

(d) 75% of the time at least 80% of the components will be usable; and

(e) that 75% of the time there will be no more than 95% of the components will be usable.

a. Construct a cumulative distribution table and graph of the probability of yield (number of usable components) yield.

b. Construct a simulation to determine the optimum decision.

c. Construct a decision tree to determine the optimum decision.

d. Compare and contrast the two methods