ASSIGNMENT: ANALYTICAL DECISION MAKING
1. Use the simplex method to solve the following Linear programming model (LP) problem:
Max Z = 2x1 + 3x2 + 3x3
Subject to: 3x1 + 2x2≤ 60
-x1 + x2 + 4x3≤ 10
2x1 - 2x2 + 5x3≤ 50
x1 , x2 , x3 0
2. A company with three factories (X,Y,Z) and five warehouses (A,B,C,D,E) indifferent locations has the transportation costs (in Naira) from factories towarehouses. Factory capacities and
warehouse requirements are stated below:
|
Factories
|
Warehouses
|
Factory Capacity
|
|
A
|
B
|
C
|
D
|
E
|
|
X
|
5
|
8
|
6
|
4
|
3
|
800
|
|
Y
|
4
|
7
|
8
|
6
|
5
|
600
|
|
Z
|
8
|
4
|
7
|
5
|
6
|
1,100
|
|
Warehouse requirements
|
350
|
425
|
500
|
650
|
575
|
2,500
|
Determine the optimal solution for this model.
2. Building a swimming pool consists of nine major activities. The activities and their immediate predecessor are shown below;
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
|
Immediate predecessor
|
-
|
-
|
A,B
|
A,B
|
B
|
C
|
D
|
D,F
|
E,G,H
|
|
Optimistic
|
3
|
2
|
5
|
7
|
2
|
1
|
5
|
6
|
3
|
|
Most probable
|
5
|
4
|
6
|
9
|
4
|
2
|
8
|
8
|
4
|
|
Pessimistic
|
6
|
6
|
7
|
10
|
6
|
3
|
10
|
10
|
5
|
a) Draw the project network.
b) What are the critical activities?
c) What is the expected time to complete the project?
d) What is the probability that the project can be completed in 25 weeks or fewer days?
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.