Operations Management techniques

Topics: Linear programming, Optimization, Pennsylvania Railroad locomotives Pages: 7 (944 words) Published: December 3, 2013

FACULTY OF MANAGEMENT

DEPARTMENT OF QUALITY AND OPERATIONS MANAGEMENT

PROGRAMME : NATIONAL DIPLOMA
OPERATIONS MANAGEMENT

SUBJECT:OPERATIONS MANAGEMENT
TECHNIQUES III

CODE:BPI33A3

DATE : 16 APRIL2012

DURATION:1 HOUR

TOTAL MARKS:50

WEIGHT : 20
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EXTERNAL MODERATOR: (Dr) J VERMEULEN

NUMBER OF PAGES : 3 PAGES
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INSTRUCTIONS TO CANDIDATES:

This is a closed book assessment.
Leave margins and spaces between the questions.
Unless otherwise indicated, express your answers correct to two (2) decimal places.
Where appropriate, indicate the units of your answer. (e.g. Hour, R )
NOTE: Marks will be awarded for theoretical knowledge, application of the theory and use of relevant examples. The general University of Johannesburg policies, procedures and rules pertaining to written assessments apply to this assessment.

QUESTION 1 [22]

The tableau below is the final simplex tableau for a LP model, where S1 and S2 are slack variables added to the original problem: Cj

Solution
MixR10R30R0R0Quantity
X1X2S1S2
R10X11420160
R0S206-71200
ZjR10R40R20R0R1600
Cj – Zj0-10-200

What is the range of optimality for the contribution rate of the variable X1 and X2 ? (12)
How much would you be willing to pay for one more unit of the first resource, which is represented by slack variable S1?(2)
What is the value of one more unit of the second resource? Why?(2)
What would the optimal solution be if the profit on X2 were changed to R35 instead of R30?(2)
What would the optimal solution be if the profit on X1 were changed to R12 instead of R10?(2)
How much could the right-hand side in constraint number 2 (q2) be decreased before profit would be affected?(2)

QUESTION 2 [21]

A manufacturing firm produces electric motors for washing machines and vacuum cleaners. The firm has resource constraints for production time, steel, and wire. The linear programming model for determining the number of washing machine motors (x1) and vacuum cleaner motors (x2) to produce has been formulated as follows.

maximize P = 70x1 + 80x2 (profit, R)

subject to
2x1 + x2 ≤ 19 (production, hr)
x1 + x2 ≤ 14 (steel, kg)
x1 + 2 x2 ≤ 20 (wire, m)
x1 , x2 ≥ 0

The final optimal simplex tableau for this model is as follows.

Сј Basic 6 10 0 0 0 Variables Quantity x1 x2 s1 s2 s3 70

0
80 x1

x2 6
1
71
0
00
0
1 2/3
-1/3
-1/30
1
0-1/3
-1/3
2/3

сј­zј 9807080 200 30
00-200- 30

2.1Formulate the dual for this problem (4) 2.2Define the dual variables. (3) 2.2Determine the feasible ranges for q1 (production hours), q2(kilograms of steel), and q3 (meters of wire)....