- Solve the following linear program using the simplex algorithm:
maxz = 10x1 + 6x2 + 4x3
subject to
4x1 + 5x2 + 2x3 + x4 20 3x1 + 4x2 x3 + x4 30 x1, x2, x3, x4 0
- Solve the following linear program using the simplex algorithm: (careful: is this linear program in standard form?)
minz = 7x1 8x2
subject to
4x1 + x2 100 2x1 2x2 160 x1 40 x1, x2 0
Draw the region of feasible solution to this problem and indicate the solution you get at each step of the simplex algorithm.
2
- Solve the following linear program using the simplex algorithm and a suitable auxiliary program:
maxz = 2x1 + 6x2
subject to
x1 x2 3 3x1 + 3x2 3 x1 + 2x2 2 x1, x2 0 optional: Use the graphical method to find the region of feasible solutions.
- Solve the following linear program using the simplex algorithm and a suitable auxiliary program: (careful: is this linear program in standard form?)
minz = 2x1 3x2 4x3
subject to
2x2 + 3x3 5 x1 + x2 + 2x3 4 x1 + 2x2 + 3x3 7 x1, x2, x3 0
- Explain why the following dictionary cannot be the optimal dictionary for any linear programming problem in which w1 and w2 are the initial slack variables:
| z | = | 4 | w1 | 2x2 |
| x1 | = | 3 | 2x2 | |
| w2 | = | 1 | +w1 | 2x2 |
Hint: If it could, what was the original problem from which it came?
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