Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited so at most 8 will be produced.
The following is the LP model for this problem.
Let X1 = Number of Beds to produce
X2 = Number of Desks to produce
MAX: 30 X1 + 40 X2
Subject to: 6 X1 + 4 X2 £ 36 (carpentry)
4 X1 + 8 X2 £ 40 (varnishing)
X2 £ 8 (demand for X2)
X1, X2 ³ 0
The Solver created the Sensitivity Report for the above LP problem.
Changing Cells

Constraints

Note: You have to use the information provided above to answer all questions of this problem. You are not allowed to use Solver software to resolve the model.
Please provide brief answers to the following FIVE questions based on the report.
a. How much can the price of Beds drop before the current optimal solution changes?
b. The constraint of Carpentry hours has a shadow price of 2.5. What does this value imply?
c. Suppose the company can purchase additional 5 varnishing hours for $20. Should the company pay to buy the hours? Why?
d. Suppose the company can increase the unit profit of Desks to $50. What is the resulting optimal objective function value?
e. Suppose the company can increase the demand for Desks by some marketing effort. Does it help the company to increase the total profit? Why?

Transcribed Image Text:

Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease Number to make: SBS4 30 30 10 Number to make: SCS4 40 20 20 Final Shadow Constraint Allowable Allowable Cell Name SDS8 Carpentry Used 36 2.5 36 SDS9 Vamishing Used 4 3.7540 SDS10 Desk demand Used 3 0 Value Price R.H. Side Increase Decrease 24 26.67 16 1E+30 5 16