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## #1 2006-07-28 07:21:46

Prakash Panneer
Member
Registered: 2006-06-01
Posts: 110

Question

Malik Carpets Sdn Bhd produces two popular grades of commercial carpeting among its many other products. In the coming production period, Malik has to decide how many rolls of each grade of commercial carpet to produce in order to maximize profit.

Each roll of Grade I carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade II carpet uses 40 units of synthetic fiber, requires 28 hours of production time and needs 15 units of foam backing.

The profit per roll of Grade I carpet is RM200 and the profit per roll of Grade II carpet is RM160. In the coming production period, Malik has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time . The company has 1500 units of foam backing available for use.

The simplex method was used to solve the problem and the final simplex table is proved below.

Table:
C j    Basic Variables       \$200.00    160    0    0    0     RHS
X1    X2    S1    S2    S3
200    X1                             1    0.8    0.02    0    0    60
0    S2                                0    8    -0.5    1    0    300
0    S3                                0    -1    -0.4    0    1    300
Z j                                200    160    4    0    0    12000
C j - Z j                           0    0    -4    0    0

Sorry, I can't Draw a table Clearly. Can anyone help me?
...............................

1.  Formulate the above as a Linear programming problem with the objective of maximizing profits.

2. Set up the initial simplex table for the above problem.

3. State the optimum output mix and the maximum profit attainable.

4. Are there any unused resource? If so state which and how much of the resource is not fully utilized?

5. What is the range of optimality for X1?

6. Determine the Range of Indifference for X2?

7. If Malik can obtain additional units of synthetic fiber for a premium of RM10 per unit, is it worthwhile for him to acquire additional synthetic fiber?

8. What will happen to the maximum profit and the output of Grade I rolls if Malik were to produce 30 rolls of the Grade II  carpet. What is the implication of your answer?

9. Carry out a sensitivity analysis on the RHS value for the synthetic fiber constraint.

Letter, number, arts and science
of living kinds, both are the eyes.

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## #2 2006-08-04 11:51:53

Prakash Panneer
Member
Registered: 2006-06-01
Posts: 110

Letter, number, arts and science
of living kinds, both are the eyes.

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## #3 2006-08-07 12:08:02

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Table:
I'm just trying to neaten the table as you have asked.

C     j    Basic Variables \$200.00    160    0    0    0   RHS
X1        X2    S1     S2   S3
200 X1                             1        0.8    0.02   0    0       60
0    S2                             0         8    -0.5     1     0      300
0    S3                             0        -1    -0.4     0     1      300
Z    j                               200    160    4        0    0      12000
C j  -Z j                           0         0      -4      0    0

igloo myrtilles fourmis

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## #4 2006-08-07 12:14:00

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Try using the code tags to line up text(I'd do it for you, but I don't know if I'd make the table different from what you wanted).

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## #5 2006-08-09 09:00:46

Prakash Panneer
Member
Registered: 2006-06-01
Posts: 110

Can anyone help me?