Question: David, LaDeana, and Lydia are the sole partners and workers in a company that produces fine clocks. David and LaDeana are each available to work

a maximum of 40 hours per week at the company, while Lydia is available to work a  maximum of 20 hours per week.

The company makes 2 different types of clocks: a grandfather clock and a wall clock. To make a clock, David assembles the inside mechanical parts of the

clock while LaDeana produces the hand carved wood casings. Lydia is responsible for taking orders and shopping the clocks. The amount of time required

for each of these tasks is shown next

Time Required

Task Grandfather Clock Wall Clock

Assemble Clock Mechanism 6 hours 4 hours

Carve wood casing 8 hours 4 hours

Shipping 3 hours 3 hours

Each grandfather clock built and shipped yields a profit of $300, while each wall clock yields a profit of $200. The 3 partners now want to determine how many

clocks of each type should be produced per week to maximize profits.

1. Formulate a linear programming model in algebraic form for this problem

C) Formulate and solve the original version of this model on a spreadsheet.

G)For each of the 3 partners in turn, use the Excel Solver to determine the effect on the optimal solution and the total profit if that partner alone were

to increase his or her maximum number of work hours available per week by 5 hours.

1. Generate the Excel Sensitivity report and use it to determine the allowable range for the unit profit for each type of clock and

the allowable range for the maximum number of hours each partner is available to work per week.

J) To increase the total profit, the 3 partners have agreed that one of them will slightly increase the maximum number of hours available to work per week.

The choice of which one will be based on which one would increase the total profit the most. Use the sensitivity report to make this choice.

K) Explain why one of the shadow prices is equal to zero.

L) Can the shadow prices in the sensitivity report be validly used to determine the effect if Lydia were to change her maximum number of hours available to work from 40 to 35.

M) Repeat part L if, in addition to the change for Lydia, David also were to change his maximum number of hours available to work per week from 40 to 35.

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Solution: The downloadable solution consists of 5 pages
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