The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives.

State of Nature

Decision Alternative

s$1$

s$2$

d$1$

$112$

d$2$

$54$

$($a$)$

Suppose

P$($s$1)=0\mathrm{.}2$

and

P$($s$2)=0\mathrm{.}8.$

What is the best decision using the expected value approach?

The best decision is

d$$

with an expected value of

$.$

$($b$)$

Perform sensitivity analysis on the payoffs for decision alternative

d$1.$

Assume the probabilities are as given in part $($a$),$ and find the range of payoffs under states of nature

s$1$

and

s$2$

that will keep the solution found in part $($a$)$ optimal.

As long as the payoff for

s$1$

under

d$1$

is

$--?--$

$,$ then the solution found in part $($a$)$ will be optimal.

As long as the payoff for

s$2$

under

d$1$

is

$--?--$

$,$ then the solution found in part $($a$)$ will be optimal.

Is the solution more sensitive to the payoff under state of nature

s$1$

or

s$2?$

s$1$

s$2$