Note: Write the formula for every question depending upon the requirement
Question 1: 15 marks
A toy manufacturing company makes a plastic tricycle that is composed of three major
components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels.
The company has orders for 15,000 of these tricycles. Current schedules yield the following
information.
Requirements
Plastic
2
4
.75
50000 Component
Front
Seat/Frame
Rear wheel (each)
Available Time
9
7
3
160000 Space
2
2
.1
30000 Cost to
Manufacture
9
5
2 Cost to
Purchase
15
10
5 The company obviously does not have the resources available to manufacture everything
needed for the completion of 15000 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
16000 fully completed tricycles at the minimum cost.
What are the decision variables, objective function, constraints ?
Question 2: 15 marks
The distribution system for a Herman Company consists of three plants, two warehouses and
four customers. Plant capacities and shipping costs (€) from each plant to each warehouse are
given below:
Plant
Warehouse
1
2
Capacity
1
7
4
600
2
8
5
380
3
6
7
700
Customer demand and shipping costs per unit in € from each warehouse to each customer
are given in the table below:
Warehouse
1
2
Demand 1
3
5
500 2
4
7
400 Customer
3
8
6
300 4
7
4
480 a. Draw a network model of this problem.
b. Develop the linear program for this problem.
Page 1 of 2 Question 3: 20 marks
Given the following details of activities and times estimated in days,
Activit
y
A
B
C
D
E
F
G
H
I
J
K Precedenc
e
Activities
------A
A
A, B
C
C
E, F, G
H
D, J Optimistic Most
Probable Pessimistic 2
1
6
5
3
8
4
2
5
12
2 5
3
7
12
4
9
6
6
7
13
3 6
7
10
14
5
12
8
9
12
14
4 a. What are the critical path activities?
b. What is the expected time to complete the project?
c. What is the probability the project will take more than 32 days to complete? Page 2 of 2

 

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