ADM$2302$: Business Analytics Final Exam $$ Fall $2015$ Page $2$ of $13$ Problem $1$ Sensitivity Analysis $(14$ points$)$ Colonial Furniture produces hand$-$crafted colonial style furniture. Plans are now being made for the production of rocking chairs, dining room tables, and$/$ or armoires over the next week. These products go through two stages of production $($assembly and finishing$).$ The following table gives the time required for each item to go through these two stages, the amount of wood required $($fine cherry wood$),$ and the corresponding unit profits, along with the amount each resource is available next week. Rocking Chair Dining Room Table Armoire Available Assembly $($minutes$)1001801203600$ Finishing $($minutes$)6080802000$ Wood $($pounds$)301801204000$ Unit profit $$240$ $$720$ $$600$ A linear programming model has been formulated in a spreadsheet to determine the production levels that would maximize profit. The solved spreadsheet model, the algebraic formulation and corresponding sensitivity report are shown below. Formulation: Let R$,$ D and A$,$ denote the number of units of Rocking Chair, Dining Room Table and Armoire $($respectively$)$ to produce. Max Profits $($$$)$ Z $=240$R $+720$D $+600$A Subject to: $1.$ Assembly: $100+180+120<=36002.$ Finishing: $60+80+80<=20003.$ Wood: $30+180+120<=40004.$ Non$-$negativity: $,,>=0$ Spreadsheet: Rocking Chair Dining Room Table Armoire Unit Profit $$240$ $$720$ $$600$ Total Profit Production $0101516200$ Resource Required per Unit Used Sign Available Assembly $($minutes$)1001801203600<=3600$ Finishing $($minutes$)6080802000<=2000$ Wood $($pounds$)301801203600<=4000$ Sensitivity Report: Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$$3$ Production Rocking Chair $0-2302402301$E$+30$ $C$$3$ Production Dining Room Table $100720180120$ $D$$3$ Production Armoire $150600120120$ Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R$.$H$.$ Side Increase Decrease $E$$6$ Assembly $($minutes$)$ Used $360023600400600$ $E$$7$ Finishing $($minutes$)$ Used $20004\mathrm{.}52000400400$ $E$$8$ Wood $($pounds$)$ Used $3600040001$E$+30400$