Jumpin' Java Coffee Company $($JJCC$)$ operates a chain of drive$-$thru coffee shops and has decided to open a new shop across from the Oregon State University campus. The demand is expected to be either weak $($its probability of $0\mathrm{.}20$ or $20\%),$ fair $($probability of $0\mathrm{.}55$ or $55\%),$ or strong.

If the company installs 'a small booth' that only sells coffee, the associated payoffs are estimated to be $-$$$50,000,$$$10,000,$ and $$75,000$ for weak, fair, and strong demand cases, respectively. If the company chooses 'a larger facility' that also offers sandwiches and pastries, it must rent additional space and build a kitchen. The payoffs for 'a larger facility' option for the three different levels $($weak$,$ fair, and strong$)$ of demand are estimated to be $-$$$125,000,-$$$10,000,$ and $$200,000,$ respectively.

Noah Elvah Lott, JJCC$\text{'}$s operations manager has proposed another option. If 'a small booth' is chosen and demand turns out to be strong, they could then still choose to expand the shop for an expected payoff of $$125,000($instead of the estimated $$75,000,$ if no further action is taken$).$

Based on the above information, $($a$)$ draw a decision tree $($including using proper shapes of nodes and pruning the branches for the option$($s$)$ you will decide to discard. Here, make sure to label and assign values $($i$.$e$.,$ payoffs, probabilities, and the EMVs for the individual options$)$ appropriately within the decision tree$)(5$ pts$.)$ and $($b$)$ indicate clearly your final choice based on the decision tree analysis $(1$ pt$.).$

Note. In answering the above questions, please use a blank paper sheet and upload the worksheet back onto here in Canvas. Good luck!!

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