Consider the following mixed-integer linear program: Max $1x_1 + 1x_2$ s.t. $7x_1 + 9x_2 \leq 63$ $9x_1 + 5x_2 \leq 45$ $3x_1 + 1x_2 \leq 12$ $x_1, x_2 \geq 0$ and $x_2$ integer a. Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions. b. Find the optimal solution to the LP Relaxation. Round the value of $x_2$ down to find a feasible mixed-integer solution. Specify upper and lower bounds on the value of the optimal solution to the mixed-integer linear program. c. Find the optimal solution to the mixed-integer linear program.
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First, let's rewrite the constraints in a more readable format: Maximize: z = Ix1 + x2 Subject to: Tx1 + 9x2 = 63 9x1 + Sx2 = 45 3x1 + Tx2 = 12 x1, x2 ≥ 0 x2 is an integer Show more…
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