Problem $4-11($Algorithmic$)$

Following is the payoff table for the Pittsburgh Development Corporation $($PDC$)$ Condominium Project. Amounts are in millions of dollars.

State of Nature

Decision Alternative Strong Demand S$1$ Weak Demand S$2$

Small complex, d$176$

Medium complex, d$2126$

Large complex, d$319-9$

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 $0\mathrm{.}8$ that demand will be strong $($S$1)$ and a corresponding probability of $0\mathrm{.}2$ that demand will be weak $($S$2).$ 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 $$15\mathrm{.}75$ million and as long as the payoff for the weak demand was greater than or equal to $-$$$22$ million.

Consider the medium complex decision. How much could the payoff under strong demand increase and still keep decision alternative d$3$ 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 $ fill in the blank $1$ 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 d$3$ 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 $ fill in the blank $2$ million, the large complex remains the best decision.