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Discrete Mathematics 3 - (AL_KCENG_7_3) 40536
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Cj |
|
| 30 | 24 | 12 | 0 | 0 | 0 |
Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
0 | S1 | 360 | 12 | 9 | 6 | 1 | 0 | 0 |
0 | S2 | 200 | 20 | 10 | 5 | 0 | 1 | 0 |
0 | S3 | 150 | 10 | 15 | 25 | 0 | 0 | 1 |
| Zj | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Cj - Zj |
| 30 | 24 | 12 | 0 | 0 | 0 |
Perform one iteration of the simplex method on the data in the table above and hence determine the values of the constants A, B and C in the table below.
Cj |
|
| 30 | 24 | 12 | 0 | 0 | 0 |
Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
0 | S1 | 240 | 0 | 3 | 3 | 1 | 0 | 0 |
30 | X1 | 10 | 1 | 0.5 | 0.25 | 0 | 0.05 | 0 |
0 | S3 | A | 0 | B | C | 0 | -0.5 | 1 |
| Zj | 300 | 30 | 15 | 7.5 | 0 | 1.5 | 0 |
| Cj - Zj |
| 0 | 9 | 4.5 | 0 | -1.5 | 0 |
S1 is the slack variable relating to assembly, S2 is the slack variable relating to testing and S3 is the slack variable relating to packaging.
Perform one iteration of the simplex method on the data below and determine the shadow-price for assembly.
Cj |
|
| 30 | 24 | 12 | 0 | 0 | 0 |
Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
30 | X1 | 100 | 1 | 0.5 | 0.8 | 0.25 | 0 | 0 |
0 | S2 | 80 | 0 | 2 | 2 | 0.6 | 1 | 0 |
0 | S3 | 300 | 0 | 6 | 9 | 0.25 | 0 | 1 |
| Zj | 3000 | 30 | 15 | 24 | 7.5 | 0 | 0 |
| Cj - Zj |
| 0 | 9 | -12 | -7.5 | 0 | 0 |
A company produces three types of disk drive. X1 is the number of type-A units, X2 is the number of type-B units and X3 is the number of type-C units made by the company each day. Each unit of type-A makes €30 profit, each type-B unit makes €24 profit and each type-C unit makes €12 profit.
The table below represents the final table in the simplex method with values given in euro.
S1 is the slack variable relating to assembly, S2 is the slack variable relating to packaging and S3 is the slack variable relating to distribution.
If k is the original right hand side value for packaging then its range is Calculate .
Cj |
|
| 30 | 24 | 12 | 0 | 0 | 0 |
Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
30 | X1 | 8 | 1 | 0 | 0.4 | 0.5 | -0.2 | 0 |
24 | X2 | 4 | 0 | 1 | 1 | -0.5 | 0.5 | 0 |
0 | S3 | 29 | 0 | 0 | 5 | 0.8 | 2 | 1 |
| Zj | 336 | 30 | 24 | 36 | 25.2 | 58.4 | 0 |
| Cj - Zj |
| 0 | 0 | -24 | -25.2 | -58.4 | 0 |
A company produces three types of power supply. X1 is the number of type-A units, X2 is the number of type-B units and X3 is the number of type-C units made by the company each day. Each unit of type-A makes €30 profit, each type-B unit makes €24 profit and each type-c unit makes €12 profit.
The table below represents the final table in the simplex method with values given in euro.
S1 is the slack variable relating to assembly, S2 is the slack variable relating to soldering and S3 is the slack variable relating to packaging.
What is the shadow-price for soldering?
Cj |
|
| 30 | 24 | 12 | 0 | 0 | 0 |
Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
30 | X1 | 80 | 1 | 0 | 0.3 | 0.35 | -0.25 | 0 |
24 | X2 | 40 | 0 | 1 | 1 | -0.1 | 0.5 | 0 |
0 | S3 | 60 | 0 | 0 | 3 | 1 | -3 | 1 |
| Zj | 3360 | 30 | 24 | 33 | 8.1 | 4.5 | 0 |
| Cj - Zj |
| 0 | 0 | -21 | -8.1 | -4.5 | 0 |
A company produces three types of diskdrive. X1 is the number of type-A units, X2 is the number of type-B units and X3 is the number of type-C units made by the company each day. Each unit of type-A makes €10 profit, each type-B unit makes €16 profit and each type-c unit makes €32 profit.
From the table below determine the number of type-A units the company should produce in order to maximise profit.
Cj |
|
| 10 | 16 | 32 | 0 | 0 | 0 |
Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
32 | X3 | 40 | 0.2 | 0 | 1 | 0 | 0.2 | -0.4 |
0 | S1 | 25 | -0.5 | 0 | 0 | 1 | -0.5 | -0.6 |
16 | X2 | 48 | 0.3 | 1 | 0 | 0 | 0.4 | 1.4 |
| Zj | 2298 | 11.2 | 16 | 32 | 0 | 7.8 | 3.6 |
| Cj - Zj |
| -1.2 | 0 | 0 | 0 | -7.8 | -3.6 |
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