Problem 2 (Decision Tree based) - 5 POINTS Johnson's Metal (JM), a small manufacturer of metal parts, is attempting to decide whether or not 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 $40,000. If JM gets the order, an event estimated as occurring with probability 0.5, it will be possible to sell 10,000 items to Protrac for $45 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 $45,000 and the per unit production cost is $21. However, if JM uses its current machines, it runs the risk of incurring overtime costs. The relationship between overtime costs and the status of JM's other business is presented in Figure 1 below. The new forge costs $280,000. However, with the new forge, JM would certainly not incur any overtime costs, and the production cost will be only $12 per unit. Figure 1. Cost and Probability data for Johnson's Metal Problem Other Business Probability Overtime cost to JM 0.2 Heavy Normal 0.6 $200,000 100,000 0 Light 0.2 Draw a complete decision tree and then analyze this tree and state the complete set of decisions that JM needs to take. You MUST show all your work/Math just like we did in class to receive credit