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Discrete Mathematics 3 - (AL_KCENG_7_3) 40536
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The online tests constitute the continuous assessment element of this course and are therefore subject to the exam regulations of the college.
Tests are not designed as group projects. All work presented by a student will be the work of that student alone.
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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 | 0.4 | 0 | 0 |
0 | S2 | 80 | 0 | 2 | 2 | -0.2 | 1 | 0 |
0 | S3 | 300 | 0 | 6 | 9 | 0.4 | 0 | 1 |
| Zj | 3000 | 30 | 15 | 24 | 12 | 0 | 0 |
| Cj - Zj |
| 0 | 9 | -12 | -12 | 0 | 0 |
A company produces three types of mobile phone. 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.
Perform one iteration of the simplex method on the data below and hence determine the number of type-B units that must be produced in order to maximise profit.
| Cj | 30 | 24 | 12 | 0 | 0 | 0 | ||
| Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
| 24 | X2 | 20 | 0 | 1 | 0.2 | 0.5 | 0 | 0.2 |
| 0 | S2 | 10 | 0 | 0 | 0.4 | 1 | 1 | 0.6 |
| 30 | X1 | 30 | 1 | 0 | 0.2 | 0.4 | 0 | 0.5 |
| Zj | 1380 | 30 | 24 | 10.8 | 24 | 0 | 19.8 | |
| Cj - Zj | 0 | 0 | 1.2 | -24 | 0 | -19.8 |
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 €12 profit, each type-B unit makes €18 profit and each type-c unit makes €20 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.
If k is the original right hand side value for packaging then its range is Calculate correct to 2 decimal places.
Cj | 12 | 18 | 20 | 0 | 0 | 0 | ||
| Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
18 | X2 | 12 | 0 | 1 | 0 | -1 | 0.8 | -0.4 |
20 | X3 | 14 | 0 | 0 | 1 | 1 | -0.5 | -0.6 |
12 | X1 | 16 | 1 | 0 | 0 | 0.5 | 1.6 | 2.4 |
Zj | 688 | 12 | 18 | 20 | 8 | 23.6 | 9.6 | |
Cj - Zj | 0 | 0 | 0 | -8 | -23.6 | -9.6 |
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 | 14 | 0 | 0 | 1 | -0.4 | 0.2 | -0.4 |
10 | X1 | 25 | 1 | 0 | 0 | 1 | -0.5 | -0.6 |
16 | X2 | 28 | 0 | 1 | 0 | 0.5 | 0.4 | 1.4 |
| Zj | 1146 | 10 | 16 | 32 | 5.2 | 7.8 | 3.6 |
| Cj - Zj |
| 0 | 0 | 0 | -5.2 | -7.8 | -3.6 |
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.
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.
What is the shadow-price for assembly?
Cj |
|
| 10 | 16 | 32 | 0 | 0 | 0 |
Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
32 | X3 | 14 | 0 | 0 | 1 | -0.4 | 0.2 | -0.4 |
10 | X1 | 25 | 1 | 0 | 0 | 1 | -0.5 | -0.6 |
16 | X2 | 28 | 0 | 1 | 0 | 0.5 | 0.4 | 1.4 |
| Zj | 1146 | 10 | 16 | 32 | 5.2 | 7.8 | 3.6 |
| Cj - Zj |
| 0 | 0 | 0 | -5.2 | -7.8 | -3.6 |
A company produces three types of oven. 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 €40 profit and each type-c unit makes €50 profit.
Perform one iteration of the simplex method on the data below and hence determine the number of type-C ovens the company should produce inorder to maximise profits.
| Cj | 30 | 40 | 50 | 0 | 0 | 0 | ||
| Cb | Basis | b | X1 | X2 | X3 | S1 | S2 | S3 |
| 50 | X3 | 20 | 0.2 | 0 | 1 | 0.6 | 0 | 0.2 |
| 0 | S2 | 10 | 0.5 | 0 | 0 | 0.2 | 1 | -2.4 |
| 40 | X2 | 30 | 0.4 | 1 | 0 | -0.5 | 0 | 0.5 |
| Zj | 2200 | 26 | 40 | 50 | 10 | 0 | 30 | |
| Cj - Zj | 4 | 0 | 0 | -10 | 0 | -30 |