Problem
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 for 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, and the corresponding unit profits, along with the amount of each resource available.
|
|
Rocking Chair
(RC)
|
Dining Room Table (DRT)
|
Armoire
(ARM)
|
Available
|
|
Assembly (minutes)
|
100
|
180
|
120
|
3,600
|
|
Finishing (minutes)
|
60
|
80
|
80
|
2,000
|
|
Wood (pounds)
|
30
|
180
|
120
|
4,000
|
|
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 Answer Report and the Sensitivity Report from that analysis are shown here:
Answer Report:
Sensitivity Report:
For each of the following parts, answer the question as specifically and completely as possible without re-solving the problem with Solver. Note: Each part is independent (i.e., any change made in one problem part does not apply to any other parts).
A. Suppose the profit per armoire decreases by $50. Will this change the optimal production quantities? Why? Why not? Will it change the overall profit? If so, by how much?
B. Suppose that a part-time worker in the assembly department calls in sick, so that now 4 fewer hours are available that day in the assembly department. How much would this affect total profit? Would it change the optimal production quantities? Why? Why not?
C. The shadow price for the wood constraint is zero. Why is that?