:ANALYTICAL DECISION MAKING
CMS 321:ANALYTICAL DECISION MAKING
MAY-AUG 2017 ASSIGNMENT Answer ALL questions
1.Use the simplex method to solve the following Linear programming model (LP) problem:
Max Z = 2×1 + 3×2 + 3×3
Subject to: 3×1 + 2×2 ≤ 60
-x1 + x2 + 4×3 ≤ 10
2×1 – 2×2 + 5×3 ≤ 50
x1 , x2 , x3 0 (10 marks)
2.A company with three factories (X,Y,Z) and five warehouses (A,B,C,D,E) in different locations has the transportation costs (in Naira) from factories to warehouses. 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. (10 marks)
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 (4 marks)
b) What are the critical activities (2 marks)
c) What is the expected time to complete the project (2 marks)
d) What is the probability that the project can be completed in 25 weeks or fewer days (2 marks)