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 of each resource available next week.
A linear programming model has been formulated in a spreadsheet to determine the production levels that would maximize profit. The solved spreadsheet model and corresponding sensitivity report are shown below.
For each of the following parts, answer the question as specifically and completely as is 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? What can be said about the change in total profit?
b. Suppose the profit per table decreases by $60 and the profit per armoire increases by $90. Will this change the optimal production quantities? What can be said about the change in total profit?
c. Suppose a part-time worker in the assembly department calls in sick, so that now four fewer hours are available that day in the assembly department. How much would this affect total profit? Would it change the optimal production quantities?
d. Suppose one of the workers in the assembly department is also trained to do finishing. Would it be a good idea to have this worker shift some of his time from the assembly department to the finishing department? Indicate the rate at which this would increase or decrease total profit per minute shifted. How many minutes can be shifted before this rate might change?
e. The shadow price and allowable range for the wood constraint are missing from the sensitivity report. What numbers should be there? Explain how you were able to deduce each number.
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