Question

Problem 13-11 (Algorithmic) Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions dollars. State of Nature Strong Demand S1 Weak Demand S2 7 Decision Alternative Small complex, di Medium complex, d2 Large complex, d3 15 23 -7 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.78 that demand will be strong (S1) and a corresponding probability of 0.22 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17.82 million and as long as the payoff for the weak demand was greater than or equal to-$25.36 million. a. Consider the medium complex decision. How much could the payoff under strong demand increase and still keep decision alternative dz the optimal solution? If required, round your answer to two decimal places. The payoff for the medium complex under strong demand remains less than or equal to $ 15.95 X million, the large complex remains the best decision. b. Consider the small complex decision. How much could the payoff under strong demand increase and still keep decision alternative d3 the optimal solution? If required, round your answer to two decimal places. The payoff for the small complex under strong demand remains less than or equal to $ million, the large complex remains the best decision.

Answer 1

a. To determine the maximum increase in the payoff under strong demand that would still keep decision alternative d2 (medium complex) as the optimal solution, we need to find the threshold value.

From the sensitivity analysis, the threshold value for the payoff under strong demand is $17.82 million for the large complex. Therefore, the maximum increase in the payoff under strong demand for the medium complex while still keeping the large complex as the optimal solution would be $17.82 million.

b. Similarly, to find the maximum increase in the payoff under strong demand that would still keep decision alternative d3 (small complex) as the optimal solution, we need to determine the threshold value.

According to the given information, the threshold value for the payoff under strong demand is not provided for the small complex. Hence, without the specific threshold value for the small complex, we cannot determine the exact maximum increase in the payoff under strong demand while keeping the large complex as the best decision.

Please note that the value of the threshold for the small complex under strong demand is missing from the provided information.