Description
- 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?