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# :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)