Is the set of vectors{(1,2,3),(3,4,1),(2,3,2)} linearly independent? Give reason for the answer.
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A company has 5 jobs to be processed by 5 mechanics. The following table gives the return in rupees when the ith job is assigned to the jth mechanic ( i, j = 1,2,....5) . How should the jobs be assigned to the mechanics so as to maximize the overall return?
| 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|
| 1 | 22 | 28 | 30 | 18 | 30 |
| 2 | 30 | 34 | 18 | 11 | 26 |
| 3 | 31 | 17 | 23 | 20 | 27 |
| 4 | 12 | 28 | 31 | 26 | 26 |
| 5 | 19 | 23 | 30 | 25 | 29 |
For the transportation problem given below. Check whether the given basic feasible solution is optimal. If not, modify the given solution and find an optimal solution and the optimal value for the problem.
| 6 | 1 (25) | 9 | 3 (45) | 70 |
| 11 | 5 (5) | 2 (50) | 8 | 55 |
| 10 (85) | 12 (5) | 4 | 7 | 90 |
| 85 | 35 | 50 | 45 |
Solve the following LPP by simplex method.
Max z = 3x + 2y
s.t. 2x + y < 18
2x + 3y < 42
3x + y < 24
x, y < 0 .
Prove that the dual of dual of a LPP is primal LPP.
A departmental head has four subordinates, and four tasks to be performed. The subordinates differ in efficiency, and the tasks differ in their intrinsic difficulty. His estimate, of the time each subordinate would take to perform each task is given in the matrix below:
| Tasks | Subordinnate | |||
| E | F | G | H | |
| A | 18 | 26 | 17 | 11 |
| B | 13 | 28 | 14 | 26 |
| C | 38 | 19 | 18 | 15 |
| D | 19 | 26 | 24 | 10 |
Write the dual of the following LPP:
Maximize z = 2x1 + x2
Subject to x1 + 5x2 < 10
x1 + 3x2 > 6
2x1 + 2x2 < 8
x2 > 0, x1 is unrestricted in sign.
If and C = [1,2] compute A'B, AC, B'A + CB, whenever defined. If you think any of these is not defined, give reason for saying so.