A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. The

credit union can either approve or reject the loan application. If the credit union does not approve the

loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional

information, the credit union believes that there is a 5% chance that this customer will default on the

loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose

the $20,000. At a cost of $150, the bank can thoroughly investigate the customers credit record and

supply a favorable or unfavorable recommendation. Past experience indicates that in cases where the

customer did not default on the on the approved loan, the probability of receiving a favorable

recommendation on the basis of the credit investigation was 80%. Furthermore, in cases where the

customer defaulted on the approved loan, the probability of receiving a favorable recommendation on

the basis of the credit investigation was 25%.

a) Construct a decision tree to determine the course of action that should be taken by the

employee of local credit union to maximize profit using Expected Monetary Value approach.

Explicitly write the components (ie decisions, chance events) of the decision tree.

b) Present your probability computations. Why do we compute posterior probabilities?

c) Compute the Expected Value of the Investigation (Sample) Information (EVSI), what does it

mean?

d) Compute the Expected Value of the Perfect Information (EVPI). What does it mean?

\

A farmer in a fairyland owns 100 acres of land. He is going to plant each acre with cotton or wheat. Each acre planted with cotton yields $200 profit; each with wheat yields $120 profit. The labor and fertilizer used for each acre of plantation of cotton and wheat are given in the table below. 150 workers and 200 tons of fertilizer are available. 50 pts Cotton Wheat Labor (Workers) 4 4 Fertilizer (Tons) 5 3 Through the magic of the solver you obtain the following sensitivity analysis. Hint: Although the sensitivity report is provided, you need to construct the optimization model so that sensitivity report makes sense and this can help to solve the last two questions. Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $F$4 X1 37.5 0 200 1E+30 80 $G$4 X2 0 -80 120 80 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $I$11 Acreage 37.5 0 100 1E+30 62.5 $I$9 Labor (Workers) 150 50 150 10 150 $I$10 Fertilizer (Tons) 187.5 0 200 1E+30 12.5 a) What is the decision that maximizes the objective function? b) What is the value of the optimal objective function? c) How much should the wheat yield per acre profit change before the farmer decides to spare some acres for wheat? d) You can hire 5 additional workers. They cost 45 dollars for the season (timeframe of interest in the problem). Would you hire them and why? e) For the situation described in the previous question d, what would be the new objective function value? f) An individual wants to rent 50 acres for $1. Would you rent? What is your reasoning? g) The curse of plenty happens (when all farmers get a very high amount of output) and cotton prices now yield 110 dollars per acre. What should you do and why? h) After the curse of plenty, you made an adaptive decision in question q. Then, a year later cotton prices come back to be 150 dollars, what will your profit be in total?