Following is the payoff table for the Pittsburgh Development Corporation (PDC) C
ID: 466273 • Letter: F
Question
Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars.
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 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 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 $15.75 million and as long as the payoff for the weak demand was greater than or equal to -$22 million.
Consider the medium 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 medium complex under strong demand remains less than or equal to $_____ million, the large complex remains the best decision.
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.
Explanation / Answer
Question 1 Consider the medium 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.
Answer
Let the payoff for strong demand for d2 be p
Given probability for strong demand=0.8
Probability for weak demand =0.2
hence for decision alternative d3 to remain best
payoff for d3>=payoff for d2 which means
19*0.8 + (0.2)*(-9)>=p*0.8 + 0.2*6
13.4>=0.8p+1.2
0.8p <=12.2
P<=12.2/0.8=15.25
The payoff for the medium complex under strong demand remains less than or equal to $15.25 million, the large complex remains the best decision.
Question 2 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
Answer
As solved in question 1 payoff for d1<=payoff for d3
which means p*0.8+6*0.2<=19*0.8+(-9)*0.2
p<=15.25
The payoff for the small complex under strong demand remains less than or equal to $15.25 million, the large complex remains the best decision.