Question $2$:

Seat and Greet manufactures couches and love seats. Each couch contributes $$850$ to profit and each love seat,

$$650.$ The resource requirements $($square feet of fabric, cubic feet of stuffing, and number or workers to complete

an item in one day$)$ and availability are shown in the table below. Marketing considerations dictate that at least $50$

couches and at least $40$ love seats be produced.

Part A: Formulate the problem as a Linear Program.

Part B: Solve the LP $($provide exact values for all variables and the optimal objective function$).$

Hint: The optimal objective function value is $$70,450$

$[$Note$,$ I am providing this hint because having the optimal solution is necessary to do Part C$.]$

Part C: Answer the following questions from your output. $($Note$,$ do not simply rerun the model$-$use the Linear

Programming output and Sensitivity Analysis to explain your answers.$)$

i$)$ If couches contributed $$1,000$ to profit, what would be the new optimal solution to the problem $($decision

variables and objective function$)?$

ii$)$ What is the most that Seat and Greet should be willing to pay for an extra cubic foot of stuffing?

iii$)$ If Seat and Greet were required to produce at least $45$ couches, what would their profit be$?$

iv$)$ Seat and Greet is considering producing reclining chairs. A reclining chair contributes $$500$ to profit and

requires $30$ square feet of fabric, $15$ cubic feet of stuffing, and $2$ workers to produce a chair in one day. Should Seat

and Greet produce any reclining chairs? Again, do not rerun the model.