Show me the steps to solve Problem $15-18$ Algo $($Computing Branch Probabilities with Bayes' Theorem$)$

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Question Workspace

Hint$($s$)$ Check My Work

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$)$:

State of Nature

Low Demand Medium Demand High Demand

Decision Alternative s$1$ s$2$ s$3$

Manufacture, d$1-2040100$

Purchase, d$2104570$

The state$-$of$-$nature probabilities are P$($s$1)=0\mathrm{.}20,$ P$($s$2)=0\mathrm{.}20,$ and P$($s$3)=0\mathrm{.}60.$ Do not round your intermediate calculations.

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

Manufacture component part

$($b$)$ Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand. Enter your answer in thousands dollars. For example, an answer of $$200$ thousands should be entered as $200,000.$

Gorman

should

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 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$\backslash$cap s$1)+$ P$($F$\backslash$cap s$2)+$ P$($F$\backslash$cap s$3)=$ 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

$-$ Select your answer $-$

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

$

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