Assignment
Question 1:
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
|
|
|
Cost to
|
Cost to
|
|
Component
|
Plastic
|
Time
|
Space
|
Manufacture
|
Purchase
|
|
Front
|
2
|
9
|
2
|
9
|
15
|
|
Seat/Frame
|
4
|
7
|
2
|
5
|
10
|
|
Rear wheel (each)
|
.75
|
3
|
.1
|
2
|
5
|
|
Available
|
50000
|
160000
|
30000
|
|
|
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:
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
|
Customer
|
|
1
|
2
|
3
|
4
|
|
1
|
3
|
4
|
8
|
7
|
|
2
|
5
|
7
|
6
|
4
|
|
Demand
|
500
|
400
|
300
|
480
|
a. Draw a network model of this problem.
b. Develop the linear program for this problem.
Question 3:
Given the following details of activities and times estimated in days,
|
Activity
|
Precedence Activities
|
Optimistic
|
Most Probable
|
Pessimistic
|
|
A
|
---
|
2
|
5
|
6
|
|
B
|
---
|
1
|
3
|
7
|
|
C
|
---
|
6
|
7
|
10
|
|
D
|
A
|
5
|
12
|
14
|
|
E
|
A
|
3
|
4
|
5
|
|
F
|
A, B
|
8
|
9
|
12
|
|
G
|
C
|
4
|
6
|
8
|
|
H
|
C
|
2
|
6
|
9
|
|
I
|
E, F, G
|
5
|
7
|
12
|
|
J
|
H
|
12
|
13
|
14
|
|
K
|
D, J
|
2
|
3
|
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?