Problem 11-1
(a) | Indicate whether the following linear program is an all-integer linear program or a mixed-integer linear program. |
Max | 30x_{1} + 25x_{2} | |
s.t. | ||
3x_{1} + 1.5x_{2} ≤ 400 | ||
1.5x_{1} + 2x_{2} ≤ 250 | ||
1x_{1} + 1x_{2} ≤ 150 | ||
x_{1}, x_{2} ≥ 0 and x_{2} integer |
This is a mixed-integer linear program. |
Write the LP Relaxation for the problem but do not attempt to solve. | |
If required, round your answers to one decimal place. | |
Its LP Relaxation is |
Max | x_{1} + x_{2} | |
s.t. | ||
x_{1} + 1.5x_{2} ≤ | ||
1.5x_{1} + x_{2} > | ||
x_{1} + x_{2} ≤ | ||
x_{1} , x_{2} ≤ 0 and x1 integer |
(b) | Indicate whether the following linear program is an all-integer linear program or a mixed-integer linear program. |
Max | 3x_{1} + 4x_{2} | |
s.t. | ||
2x_{1} + 4x_{2} ≥ 8> | ||
2x_{1} + 6x_{2} ≥ 12 | ||
x_{1}, x_{2} ≥ 0 and integer |
This is a mixed-integer linear program. |
Write the LP Relaxation for the problem but do not attempt to solve. | |
If required, round your answers to one decimal place. | |
Its LP Relaxation is |
Max | x_{1} + x_{2} |
s.t. | |
2x_{1} + x_{2} > | |
x_{1} + 6x_{2} ≤ | |
x_{1} , x_{2} > 0 and x1 integer |
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