PTMBA DAM Final QN Rev XMzfadBZaZ
PTMBA DAM Final QN Rev XMzfadBZaZ
PTMBA DAM Final QN Rev XMzfadBZaZ
NB:
1. Answer All Four Questions
2. Use of Calculator & Excel is permitted
3. No other Software or Resource are permitted
3. Answer to each question to be started on a fresh page
4. Assume data where ever necessary and state them clearly
Question 1 Marks 10
Martin’s Service Station is considering entering the snowploughing business for the coming
winter season. Martin can purchase either a snowplow blade attachment for the station’s pick-
up truck or a new heavy-duty snowplow truck. After analysing the situation, Martin believes
that either alternative would be a profitable investment if the snowfall is heavy. Smaller profits
would result if the snowfall is moderate, and losses would result if the snowfall is light. The
following profits/losses apply.
State of nature
Decision Alternatives Heavy, s1 Moderate S2 Light, S3
Blade attachment, d1 3500 1000 -1500
New snowplow, d2 7000 2000 -9000
The probabilities for the states of nature are P(s1) = .4, P(s2) = .3, and P(s3) = .3. Suppose that
Martin decides to wait until September before making a final decision. Assessments of the
probabilities associated with a normal (N) or unseasonably cold (U) September are as follows:
The company obviously does not have the resources available to manufacture everything needed for
the completion of 12000 tricycles so has gathered purchase information for each component. Develop
a linear programming model to tell the company how many of each component should be
manufactured and how many should be purchased in order to provide 12000 fully completed tricycles
at the minimum cost. (Formulate this as a Linear Programming problem. Do not solve the
Linear Programming Problem for optimum solution)
Question 2b Marks 5
A professor has been contacted by four not-for-profit agencies that are willing to work with student
consulting teams. The agencies need help with such things as budgeting, information systems,
coordinating volunteers, and forecasting. Although each of the four student teams could work with any
of the agencies, the professor feels that there is a difference in the amount of time it would take each
group to solve each problem. The professor's estimate of the time, in days, is given in the table below.
Use Excel Solver to determine which team works with which project. All projects must be assigned and
no team can be assigned to more than one project.
Question 3a Marks 5
Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of
pens are given below.
Question 3b Marks 5
A manufacturer of steel ingots has plants at two cities, C 1 and C2.The ingots are supplied to
four markets, M1, M2, M3, and M4. The manufacturer wants to know the pattern of shipment
from each production plant to each market that would minimize the total transportation cost.
You are given the following data on capacity and demand as also the unit transportation cost.
Plant capacities (units each):
Origin 1(plant in C1) = 3000
Origin 2(plant in C2) = 1000
The management wants to determine the total transportation cost associated with the optimal
schedule. Represent the information in a transportation tableau. Formulate this as a Linear
Programming problem. (Do not solve the Transportation Problem for optimum solution)
Question 4a Marks 5
Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate
optimal solutions? Explain using graphical method.
Max 3X + 3Y
s.t. 1X + 2Y 16
1X + 1Y 10
5X + 3Y 45
X,Y 0
Question 4b Marks 5
John has collected the following information on the amount of tips he has collected from parking cars
the last seven nights.
Day Tips
1 18
2 22
3 17
4 18
5 28
6 20
7 12