Find an initial basic feasible solution to the following transportation problem by the North-West corner method. Check whether your solution is optimal.
| 6 | 4 | 1 | 5 | 14 |
| 8 | 9 | 2 | 7 | 16 |
| 4 | 3 | 6 | 2 | 5 |
| 6 | 10 | 15 | 4 |
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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 |
Prove that the dual of dual of a LPP is primal LPP.
Solve the following game by graphical method.
Determine all the basic feasible solutions to the equations
x1 + x2 + 2x3 = 4
2x1 - x2 + x3 = 2
Identify the degenerate basic feasible solutions.
Is the set of vectors{(1,2,3),(3,4,1),(2,3,2)} linearly independent? Give reason for the answer.
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 |
A firm manufactures pills in two sizes A and B. A contains 2 grains of aspirin, 5 grains of bicarbonate and 1 grains of codeine. B contains 1 grain of aspirin, 8 grains of bicarbonate and 6 grains of aspirin, 74 grains of bicarbonate and 24 grains of codeine for providing immediate effect. It is required to determine the least number of pills a patient should take to get immediate relief. Formulate the problem as a standard LPP and solve it graphically.