HW Unit $\backslash$#$8(40$ points$)$ Submit all answers via Canvas.

$1.$ The Fruit $\backslash$& Vegetable Store $(40$ points$)$

The Fruit $\backslash$& Vegetable Store is a store that specializes in selling fresh fruit and vegetables. It sells a gourmet variety of fresh tomatoes, costing $\backslash (\backslash$$ $3\mathrm{.}15\backslash )$ per pound and selling for a price of $\backslash (\backslash$$ $4\mathrm{.}35\backslash )$ per pound. The tomatoes are delivered at the beginning of a week. At the end of each week any left$-$over tomatoes are sold to a wholesaler for $\backslash (\backslash$$ $1\mathrm{.}65\backslash )$ per pound. Based on recent history, the weekly demand for the tomatoes in pounds is given by the following distribution:

The manager has decided to limit her$/$his choices to ordering either $12,15,$ or $18$ pounds of the tomatoes. She has asked you to recommend what she should do$.$ Answer the following questions.

Hint: See Unit $8$ Practice Problem $\backslash$#$1\backslash$& $2$

$($a$)$ Using Excel, but without using Data Table, construct a Payoff Matrix in terms of possible values of demand together with the corresponding probabilities of the demand. $($Submit answer in an Excel file, $5$ pts$)$

$($b$)$ Using Excel, but now using Data Table, construct a Payoff Matrix in terms of possible values of demand together with the corresponding probabilities of the demand. Please include your formula sheet. $($Submit answer in an Excel file, $\backslash (\backslash$mathbf$\{5\}\backslash )$ pts$)$

$($c$)$ Using Excel, construct the Decision Tableau for this problem. $($Submit answer in an Excel file, $5$ pts$)$

$($d$)$ Using a Scatter Chart in Excel, graph the Risk Profile of ordering $15$ pounds. $($Submit answer in an Excel file, $5$ pts$)$

$($e$)$ Graphically represent the Reverse Cumulative View of each Risk Profile in a Clustered Column Chart. For which Profit Goals does Ordering $12$ pounds give the largest probability of achieving the Goal? $($Submit answer in an Excel file, $\backslash (\backslash$mathbf$\{5\}\backslash )$ pts$)$

$($f$)$ What is the Expected Profit from ordering $12$ pounds of tomatoes? Also, what are respective Expected Profits from ordering $15$ pounds and $18$ pounds? Based on the Expected Value Criterion, which order quantity would you recommend? $($Submit answer in an Excel file, $5$ pts$)$

$($g$)$ If the owner's sole profit goal for the tomatoes was to make at least $\backslash (\backslash$$ $12\backslash ),$ which ordering quantity would you recommend? If instead the sole profit goal were $\backslash$$$15,$ which ordering quantity would you recommend? And what would you recommend if the owner's sole profit goal were $\backslash$$$20?($Submit answer in an Excel file, $5$ pts$)$

$($h$)$ Given the conflicting answers in $($ f $)$ and $($ g $)$ above, what would you recommend? Why? $($Submit answer in an Excel file, $5$ pts$)$