Question: Consider the following all-integer linear program. Max 1 x 1 + 1 x 2 s.t. 5 x 1 + 6 x 2 41 1 x

Consider the following all-integer linear program.

Max 1x1 + 1x2
s.t.
5x1 + 6x2 41
1x1 + 7x2 28
2x1 + 1x2 15

x1, x2 0 and integer

(a)

Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.

On the coordinate plane, the horizontal axis is labeled x and the vertical axis is labeled x.

A region bounded by a series of connected line segments and several points are on the graph.

  • The line segments connect the approximate points (0, 4), (4.10, 3.41), (7, 1), and (7.5, 0).
  • The region is above the horizontal axis, to the right of the vertical axis, and below the line segments.
  • All ordered pairs with integer values in the region and on its boundaries are shown.

(b)

Solve the LP Relaxation of this problem.

____________at (x1, x2) =(_____________)

(c)

Find the optimal integer solution.

____________at (x1, x2) =(_____________)

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