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Assignment 8EnerCom has a possibility to present a proposal for two important contracts.  The deadlines and preparation costs for both proposals are the following: Contract 1 Contract 2 Preparation cost $5 000 $10 000 Deadline for presentation June 1st August 1st Announcement of the winner July 1st September 1st EnerCom can realize only one of the two contracts (thus, if EnerCom obtains the first contract, it will not be allowed to present a proposal for the second contract).  However, since it takes two months for preparing a proposal, EnerCom must decide immediately which one(s) of the proposal to prepare in order for them to be ready in time (nevertheless, the decision on the level of the proposal can be delayed until the last minute). For each of the contracts, EnerCom is considering two possible levels. The following table presents, as a function of these levels, the expected profits and an estimation of the probability of obtaining the contract. Contract 1 Contract 2 Profit Probability Profit Probability Level 1 $50 000 0.5 $100 000 0.3 Level 2 $70 000 0.3 $150 000 0.1 Question 1:Represent the problem of EnerCom as a decision tree and find the optimal strategy for EnerCom if the criterion is to maximize net expected profit. Find the value of a perfect information on the amount of the lowest proposal of the competitors for Contract 1 (suppose that EnerCom would obtain the contract if it were to bid an amount exactly equal to the lowest proposal). Dates are important. You can only prepare one contract, both contracts or none at all at the beginning.Perfect info is someone opening the envelope and telling you (knowing in advance) if you are winning or not.Specify the date that you get this information, not on announcement date. It makes a difference when you get this information. It has no value if you get the information at announcement date, so compute that early.Question 2: Perform a sensitivity analysis on both the optimal strategy and the value of perfect information according to the risk tolerance of EnerCom, assuming that the utility of the firm is exponential. Use the exponential utility a, b, r..risk tolerance is r. choose any value of r, at least 5, and calculate the sensitivity.EnerCom would like to have a better idea of the probability of obtaining Contract 1 as a function of the submission level. Three competitors of EnerCom are expected to submit a proposal. Here is the evaluation by EnerCom of the situation of each of its competitor, based on information about their cost structure, risk aversion and other activities. Competitor A: This competitor already is working on several current contracts and will only be interested in getting Contract 1 if its expected profit is very interesting. EnerCom evaluates that the probability that Competitor A submit a proposal at $100000 is 20%, while the probability that it submits a proposal at $125 000 is 50% and 30% at $150000.Competitor B: This competitor is interested in obtaining the contract, even at a loss, because it wants to increase its expertise and notoriety. EnerCom feels that the most probable value of Competitor B’s proposal is $95 000 and that the minimum and maximum values are respectively $80 000 and $125000.Competitor C: EnerCom reckons that the amount of the proposal of this competitor has as much chance taking any value in the interval $100 000 to $150000.Question 3:  Monte Carlo simulation…Graph the probability distribution of the lowest bid by the competitors of EnerCom. What is the probability that EnerCom obtain Contract 1 if it chooses to bid at $99000? At $130000? no longer about talking about level 1 or level 2..Question 4:Suppose that the expected costs to realize Contract 1 are $75000. Represent the expected profit of EnerCom as a function of the level of the proposal and find the optimal amount for this proposal, assuming EnerCom is risk neutral and has decided not to bid for Contract 2.Question 5: What is the optimal level of the proposal for Contract 1 if EnerCom is risk neutral and has decided to prepare a proposal for Contract 2 (Level 1 or Level 2)? Question 6: What is the optimal strategy for EnerCom assuming that its utility is described by an exponential utility function with a risk tolerance of $30,000?