Resource Allocation
ACC 341, Fall 2015
Pillercat, Inc. produces several types of heavy
equipment. Two of its products, the R-1
and the R-2, are produced in the same departments with the same equipment. Management must recommend the quantities of
R1 and R2 to produce in May, based on the following information:
1.
Pillercat’s marketing manager has judged that at
current market prices, the firm cannot sell more than 12 R-1s and 12 R-2s per
month.
2.
Contribution margins are $10,000 for each R-1 and
$8,000 for each R-2.
3.
There are two production departments, A and B. Each R-1 uses 10 hours of machining in Dept.
A and 20 hours of machining in Dept. B.
Each R-2 uses 15 hours of machining in Dept. A and 10 hours in Dept.
B. Total machining hours available
during the month are 150 in Dept. A and 160 in Dept. B.
4.
Quality testing is performed in a third
department. Each R-1 receives 30 hours
of testing, and each R-2 receives 10 hours of testing. Total testing hours available are 175.
5.
In order to maintain the current market position, top
management has decided that it is necessary to produce at least two R-2s
for every R-1 produced.
6.
A major customer has ordered a total of five R-1s and
R-2s (in any combination; for example 4 R-1s and 1 R-2, or 2 R-1s and 3 R-2s,
etc.) for next month. Thus, a total of
at least 5 R-1s and R-2s must be produced.
Requirement 1
1.
What is the linear programing model (i.e., equations
for the objective function and the constraint functions)?
2.
What are the optimal production quantities of R1 and R2
for May? Non-integer solutions—for
example, 5.4 R-1s—are okay. (The firm can start a unit and get 40% of the way
through the production process in May, and finish it in June.)
3.
What is the total contribution margin if this product mix
is produced and sold?
4.
Why should Pillercat produce more R2s when R1 has a
higher unit contribution margin? (Don’t just say, “Because this yields a higher
total profit.” Explain in terms of the
production process and/or customer demand. If both production and demand are
relevant, then include both in your explanation.)
Requirement 2
Market demand is higher than Pillercat’s optimal production
quantities in Requirement 1. If the Pillercat
expands its production facilities, then perhaps it could make a higher
profit. Suppose that adding 50 hours of
capacity in any one or more of the
three departments—A, B, or Quality—would add $5,000 to monthly fixed
costs.
Management is deciding whether or not to add 50 hours of
capacity to Department A, Department B, Quality Testing, or split the 50 hours
such that A would get 20 hours and B and Quality would each get 15 hours.
1.
Should Pillercat add the 50 hours of capacity?
2.
If yes, then should it add the 50 hours to A, B,
Quality, or split the 50 hours among the three departments?
3.
In terms of customer demand and/or production
efficiency, why is the choice you
made in question 2 the most profitable?
Deliverables
1.
Write brief answers to each of the questions in the two
Requirements above.
2.
Attach your linear programming model and Answer Reports
from Solver to support your answers in Requirements 1 and 2. You should have one Answer Report for Requirement
1 and four for Requirement 2 (one for each of the four alternatives that the
firm is considering).
