Dry Creek Wine delivers wine boxes to interested connoisseurs. They offer four gourmet wine assortments: $$Four Wines$,$Awesome $($OSM$)$ Red$,$Whites$,$ and $$Party Time$,$ each at a different price. Each of the boxes consists of a different combination of wines. The following is the Sensitivity Report obtained from running Dry Creek$$s optimization model.

Variable Cell

Cell

$C$$10$ $D$$10$ $E$$10$ $F$$10$

Name

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease

$400178117\mathrm{.}501810165001618$

$0-2\mathrm{.}5192\mathrm{.}5$ Y

Final Shadow Constraint Allowable Allowable

Constraints

$C$$15$ $C$$16$ $C$$17$ $C$$18$

Four Wines OSM Red Whites & A Red Party Time

Name

Pinot Bottles Malbec Bottles Sauvignon Blanc Bottles Riesling Bottles

Value Price

$25041502180$ X$11803$

Cell

R$.$H$.$ Side

$250150225$ X$4$

Increase Decrease

$807010080$ X$2$ X$34580$

Table $3-$ Sensitivity Report obtained from Dry Creek$$s optimization model

Answer the following questions based on the report. Treat each question independently from the rest.

Multiple Choice Questions $/$ Answers:

$1.(2$ points$)$ Is Dry Creek solving a maximization problem?

a$)$ It is a minimization problem, since the constraint $$Pinot Bottles$$ is $>=$ and its

shadow price is positive

b$)$ It is a maximization problem, since the constraint $$Pinot Bottles$$ is $>=$ and its

shadow price is positive

c$)$ It is a minimization, since the reduced cost of $$Party Time$$ is negative

d$)$ Itisamaximization,sincethereducedcostof$$PartyTime$$isnegative

e$)$ We cannot really tell, we need more information.

$2.(2$ points$)$What is the value of X$1?$ a$)0$

b$)45$ c$)180$ d$)225$ e$)+\backslash$infty

$3.(2$ points$)$What is the value of X$2?$ a$)0$

b$)45$ c$)180$ d$)225$ e$)+\backslash$infty

$4.(2$ points$)$What is the value of X$3?$ a$)0$

b$)45$ c$)180$ d$)225$ e$)+\backslash$infty

$5.(2$ points$)$What is the value of X$4?$ a$)0$

b$)45$ c$)180$ d$)225$ e$)+\backslash$infty

$6.(2$ points$)$ What is the value of Y$?$

a$)0$

b$)2\mathrm{.}5$

c$)19$

d$)+\backslash$infty

e$)$ We do not have enough information to tell

$7.(2$ points$)$ Suppose Dry Creek can take an action that would increase the right$-$hand side of any of their constraints by $40$ bottles. Which right$-$hand side should they prefer increasing?

a$)$ Pinot

b$)$ Malbec

c$)$ Sauvignon Blanc

d$)$ Riesling

e$)$ We cannot tell from the information provided

$8.(2$ points$)$ A partner from Oregon is interested in purchasing $40$ bottles of Malbec for a total of $$100.$ Is this a good proposition for Dry Creek?

a$)$ Yes, it is a good deal because Dry Creek would earn an additional $$4000$ over what they are currently earning.

b$)$ Yes,itisagooddealbecauseDryCreekwouldearnanadditional$$100$overwhat they are currently earning.

c$)$ Yes, it is a good deal because Dry Creek would earn an additional $$20$ over what they are currently earning.

d$)$ No$,$itisnotagooddealbecauseDryCreekwouldearn$$100$lessthanwhatthey are currently earning.

e$)$ No$,$ it is not a good deal because Dry Creek would earn $$20$ less than what they are currently earning.

$9.(2$ points$)$ The severe drought that California has been facing the past few years has affected the yield of Pinot wines. What is the effect of a drop of $20\%$ in the number of available Pinot bottles on the winery$$s objective function?

a$)$ A decrease of $80$

b$)$ Adecreaseof$200$

c$)$ An increase of $200$

d$)$ Anincreaseof$80$

e$)$ We cannot tell from the information provided.

$10.(2$ points$)$ You are told that the objective coefficients exactly correspond to the prices that Dry Creek is charging its customers for the various assortments of wines. What would be the impact on Dry Creek$$s objective if they charged $$20$ for $$Four Wines$?$

a$)$ No impact

b$)$ Wecannottellfromtheinformationprovided$$wemustresolvethemodel

c$)$ It would increase $120$

d$)$ Itwouldincreaseby$800$

e$)$ We cannot tell from the information provided.