Decision Mathematics 8. STEMtools inc. is a company that specializes in scientific instruments, has been invited to make a bid for a government contract. The contract calls for a specific number of instruments to be delivered during the coming year. The bids must be sealed and the lowest bid wins the contract. STEMtools estimates that it will cost 5,000 to prepare a bid, and 95,000 to supply the instruments if it wins the contract. Management at STEMtools have estimated that if there is competition then the possible low bids with associated probability are as for the following table. Low Bid Less than 115,000 Between 115,000 and 120,000 Between 120,000 and 125,000 Greater than 125,000 Probability 0.2 0.4 0.3 0.1 Your task is to make a decision tree model that finds the expected monetary value for various bidding strategies and indicates the best bidding strategy. Your answer should include the following: (a) A drawing of the decision tree. (b) Expected payoffs for leaf nodes. You can create a payoff table for STEMtools bid by competitors' low bid to illustrate how payoffs are calculated. (c) Explicit calculations for all tree nodes. (d) Advice for STEMtools management (e) Identify any assumptions that you have made in your analysis. Marks [12] Decision Mathematics 8. STEMtools inc. is a company that specializes in scientific instruments, has been invited to make a bid for a government contract. The contract calls for a specific number of instruments to be delivered during the coming year. The bids must be sealed and the lowest bid wins the contract. STEMtools estimates that it will cost 5,000 to prepare a bid, and 95,000 to supply the instruments if it wins the contract. Management at STEMtools have estimated that if there is competition then the possible low bids with associated probability are as for the following table. Low Bid Less than 115,000 Between 115,000 and 120,000 Between 120,000 and 125,000 Greater than 125,000 Probability 0.2 0.4 0.3 0.1 Your task is to make a decision tree model that finds the expected monetary value for various bidding strategies and indicates the best bidding strategy. Your answer should include the following: (a) A drawing of the decision tree. (b) Expected payoffs for leaf nodes. You can create a payoff table for STEMtools bid by competitors' low bid to illustrate how payoffs are calculated. (c) Explicit calculations for all tree nodes. (d) Advice for STEMtools management (e) Identify any assumptions that you have made in your analysis. Marks [12]