The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is

dependent on the demand for the product. The following payoff table shows the projected profit $($in thousands of dollars$)$:

The state$-$of$-$nature probabilities are $P(s_1)=0\mathrm{.}35,P(s_2)=0\mathrm{.}35,$ and $P(s_3)=0\mathrm{.}30.$ Do not round your intermediate calculations.

$($a$)$ Use a decision tree to recommend a decision.

$($b$)$ Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand. Enter your answer in thousands of dollars. For example, an answer of $$200$ thousands shou

be entered as $200,000.$

Gorman

attempt to obtain a better estimate of demand, as the additional information could be worth up to $

for Gorman.

$($c$)$ A test market study of the potential demand for the product is expected to report either a favorable $(F)$ or an unfavorable $(U)$ condition. The relevant conditional probabilities are as follows

$P(F|s_1)=0\mathrm{.}10,P(U|s_1)=0\mathrm{.}90$

$P(F|s_2)=0\mathrm{.}40,P(U|s_2)=0\mathrm{.}60$

$P(F|s_3)=0\mathrm{.}60,P(U|s_3)=0\mathrm{.}40$

What is the probability that the market research report will be favorable? $[$Hint: We can find this value by summing the joint probability values as follows: $P(F)=P(F{s}_1)+P(F{s}_2)+$

$P(F{}_3)=P(s_1)P(F|s_1)+P(s_2)P(F|s_2)+P(s_3)P(F|s_3).]$ If required, round your answer to three decimal places.

$($d$)$ What is Gorman's optimal decision strategy? Choose the correct option.

A$.$ Conduct test market, and manufacture component part, regardless of the market research report

B$.$ Conduct test market, and purchase component part, regardless of the market research report

C$.$ Conduct test market, and manufacture component part if market is favorable, or purchase component part if market is unfavorable

D$.$ Do not conduct test market, and purchase component part

E$.$ Do not conduct test market, and manufacture component part

$($e$)$ What is the expected value of the market research information? Enter your answer in thousands of dollars. For example, an answer of $$200$ thousands should be entered as $200,000.$ If your answer is zero, enter $0.$