Decision Making $-$ both DMUU & DMUR

Consider the following decision matrix presenting net profit$/$loss estimates regarding an investment project:

$\backslash$table$[[,,$DEMAND,,$],[,,$LOW,MEDIUM,HIGH$],[$EQCIIPMENTUSED$,$Small,$33,40,50],[,$Medium,$10,60,60],[,$Large,$-50,30,110]]$

Considering that the probabilities applicable to demand are not known, show the decision recommendations from the points of view of MXMX; MXMN; REALISM at Alpha$=0\mathrm{.}65$; EQL LIKE'HD; and MIN. REGRETS. Do you see a pattern? Which equipment would you choose? Explain.

Consider now that the probabilities for demand being low, medium and high have been calculated as $\mathrm{.}20,\mathrm{.}35,$ and $\mathrm{.}45,$ respectively. By using a decision tree, find the expected value $(\stackrel{}{x}$ Xbar$),$ the standard deviation $($ Sigma$),$ and the coefficient of variation $($ CoV $)$ for each size of equipment. Which size of equipment would you recommend on the basis of the three statistics that you calculated?

Referring to the Z$-$Table, calculate the probability that each alternative $($each different equipment$)$ will turn out at least a $$52$ profit? What is the likelihood that each alternative will produce a profit BETWEEN $$46$ and $$68?$

Be sure to show work, indicate the recommended alternative each time, provide a summary table $($see below$),$ and support your final statement with a reason.

$\backslash$table$[[$DMCI:$,$Reason$],[$Perfect Optimism:,$],[$Perfect Pessimism,$],[$Optimism at $={?}_{--1},],[$Equal Likelihood:,$],[$Minimizing Regret:,$]]$

Overall DMUU:

$($Give Reasons!$)$

$\backslash$table$[[,$Xbar,Sigma,CoV,$\backslash$table$[[$Normal Dist.$],[\%$