Question $3$

$5$ pts

Draw a decision tree diagram and determine the expected payoff of your optimal choice for the following scenario $($submit the decision tree in the following question$)$:

You are the new manager at Trader Dan's in Bothell. You've been tasked with growing the company. After gathering data from your colleagues in operations as well as finance, marketing and economics you've discovered the following possibilities:

These teams have pitched two locations: Everett and Bellevue. In each of these cities there's a chance that we get approved by the local governing board for a large operation $($large store stand$-$alone factory$)$ or only get approval for a small operation $($standard sized store, no factory$).$ The chance of a large operation in Everett is $40\%,$ and Bellevue is $32\%.$ The small operation is the remaining probability.

If we have a large operation, we must choose to either produce and market our full range of goods or to specialize in a specific sub$-$set of our products. Our estimated profits in Everett are $237,443$ for the full range of goods and $108,302$ for the sub$-$set and Bellevue's are $159\mathrm{.}764$ and $145,136$ respectively.

For the small operation we're stuck providing a sab$-$set of goods $($might not be the same goods as in the large operation$)$ and have a chance at a great customer turnout or a very low customer turnout. The chances of great customer turnout is $65\%$ for each city and $35\%$ for low customer turnout $($again$,$ for each city$).$ Profits for Everett are estimated to be $107,309$ and $37,736,$ for great and small turnouts respectively and Bellevue is $102,659$ and $21,807.$

Remember to DRAW A DECISION TREE diagram for the next question.

Report the EXPECTED PAYOFF of the highest paying decision, rounded to the nearest dollar for this question.

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