Question 2 (20 points) Mid-Valley Manufacturers has the opportunity to bid on a contract to sell...

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Question 2 (20 points) Mid-Valley Manufacturers has the opportunity to bid on a contract to sell the government 100,000 valves. The valves can be manufactured by Mid-Valley using existing equipment at a cost of $30 per unit. One of their engineers has suggested a new manufacturing process. If there are no complications in the development of the new process, the manufacturing cost drops to $20 per unit. If complications arise in the development of the new process, the current process will have to be used. Regardless of the outcome, it will cost $200,000 to develop the new process. There is a 0.6 chance of no complications arising in the development. Mid-Valley must make its bid before the process can be developed. They can bid a price of either $40 or $50. The probability that a $40 bid wins the contract is 0.75. The probability that a $50 bid wins the contract is 0.5. They only have one chance to bid for example, if they originally bid $50 and lose, they cannot go back with the lower bid of $40. a) Construct a decision tree for Mid-Valley, clearly indicate all probabilities and monetary values. Solve the tree to find Mid-Valley's optimal strategy? What is the expected monetary value of the optimal strategy? (12 points) 5 Question 2 (continued) b) Mid-Valley has just won the contract with a bid of $50. Before they decide whether to attempt the new process, they can do a pilot study at a cost of $50,000. The pilot study will give perfect information about whether or not there will be complications in the development of the new process. Should they do the pilot study? (8 points) 6 Question 2 (20 points) Mid-Valley Manufacturers has the opportunity to bid on a contract to sell the government 100,000 valves. The valves can be manufactured by Mid-Valley using existing equipment at a cost of $30 per unit. One of their engineers has suggested a new manufacturing process. If there are no complications in the development of the new process, the manufacturing cost drops to $20 per unit. If complications arise in the development of the new process, the current process will have to be used. Regardless of the outcome, it will cost $200,000 to develop the new process. There is a 0.6 chance of no complications arising in the development. Mid-Valley must make its bid before the process can be developed. They can bid a price of either $40 or $50. The probability that a $40 bid wins the contract is 0.75. The probability that a $50 bid wins the contract is 0.5. They only have one chance to bid for example, if they originally bid $50 and lose, they cannot go back with the lower bid of $40. a) Construct a decision tree for Mid-Valley, clearly indicate all probabilities and monetary values. Solve the tree to find Mid-Valley's optimal strategy? What is the expected monetary value of the optimal strategy? (12 points) 5 Question 2 (continued) b) Mid-Valley has just won the contract with a bid of $50. Before they decide whether to attempt the new process, they can do a pilot study at a cost of $50,000. The pilot study will give perfect information about whether or not there will be complications in the development of the new process. Should they do the pilot study? (8 points) 6