Kipling Equipment Inc. must decide to produce either a face mask or a face shield to alleviate the spread of a quickly evolving coronavirus. The face mask is disposable and developing it could potentially lead to a profit of $305,000 if competition is high or a profit of $590,000 if competition is low. The face shield, on the other hand, is reusable and has the potential of generating a fixed profit of $400,000 irrespective of high or low competition. The probability of high competition is 68% while that of low competition is 32%.

Part A Construct a decision tree or a payoff table for the decision problem and use it to answer the following questions.

a) What is the expected monetary value of the optimal decision? $

b) Based on expected monetary value, what should the Kipling do? $

c) What is the upper bound on the amount Kipling should pay for additional information? $

Part B Kipling can pay for a market survey research to better assess future market conditions. The forecast of the survey will either be encouraging or discouraging. Past records show that, given high competition, the probability of an encouraging forecast was 0.80. However, given low competition, the probability of a discouraging forecast was 0.56. Calculate posterior probabilities (to 3 decimal places) and use them to answer the following questions. Do not round intermediate probability calculations.

a) If Kipling receives an encouraging forecast from the market survey, what is the probability that they will face high competition?

b) Given Kipling receives a discouraging forecast from the market survey, what is the probability that they will face high competition?

c) If the market survey report is encouraging, what is the expected value of the optimal decision? $

d) If the market survey report is discouraging, what is the expected value of the optimal decision? $

e) What is the expected value with the sample information (EVwSI) by the market survey? $

f) What is the expected value of the sample information (EVSI) provided by the market survey? $

g) If the market survey costs $5,000, what is the best course of action for Kipling?

h) What is the efficiency of the sample information? Round % to 1 decimal place. %