Question: (10 points) Johnson's Metal (JM), a small manufacturer of metal parts, is attempting to decide whether to enter the competition to be a supplier of transmission housings for PROTRAC. In order to compete, the firm must design a test fixture for the production process and produce 10 housings that PROTRAC will test. The cost of development, that is, designing and building the fixture and the test housings, is $50,000. If JM gets the order, an event estimated as occurring with probability 0.4, it will be possible to sell 10,000 items to PROTRAC for $50 each. If JM does not get the order, the development cost is essentially lost. In order to produce the housings, JM may either use its current machines or purchase a new forge. Tooling with the current machines will cost $40,000 and the per-unit production cost is $20. However, if JM uses its current machines, it runs the risk of incurring overtime cost. The relationship between overtime costs and the status of JM's other business is presented in Figure 1. The new forge costs $260,000, including tooling costs for the transmission housings. However, with the new forge, JM would certainly not incur any overtime costs, and the production cost will be only $10 per unit. Use a decision tree to determine the optimal set of actions for JM.

FIGURE 1

Cost and Probability Data for Johnson's Metal Problem