University Ceramics manufactures plates, mugs, and steins that include the campus name and logo for sale in campus bookstores. The time required for each item to go through the two stages of production (molding and finishing), the material required (clay), and the corresponding unit profits are given in the following table, along with the amount of each resource available in the upcoming production period.
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 part does not apply to any other parts).
a. Suppose the profit per plate decreases from $3.10 to $2.80. Will this change the optimal production quantities? What can be said about the change in total profit?
b. Suppose the profit per stein increases by $0.30 and the profit per plate decreases by $0.25. Will this change the optimal production quantities? What can be said about the change in total profit?
c. Suppose a worker in the molding department calls in sick. Now eight fewer hours are available that day in the molding department. How much would this affect total profit? Would it change the optimal production quantities?
d. Suppose one of the workers in the molding department is also trained to do finishing. Would it be a good idea to have this worker shift some of her time from the molding 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 allowable decrease for the mugs’ objective coefficient and for the available clay constraint are both missing from the sensitivity report. What numbers should be there? Explain how you were able to deduce each number?
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