Question: 6. Consider the following all-integer linear program: max 5x1+8x2 s.t. 9x1 + 4x2 36 1x1 + 2x2 10 x1, x2 0 and integer. a. Graph

6. Consider the following all-integer linear program:

max 5x1+8x2 s.t. 9x1 + 4x2 36

1x1 + 2x2 10 x1, x2 0 and integer.

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

b. Find the optimal solution to the LP relaxation. Round down to find a feasible integer solution.

c. Find the optimal integer solution. Is it the same as the solution obtained in part (b) by rounding down?

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