Integer LP In-class Prob

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Presentation transcript:

Integer LP In-class Prob Consider the following mixed-integer LP. Max z = 2x1 + 3x2 s.t. 4x1 + 9x2 < 36 7x1 + 5x2 < 35 x1, x2 > 0 and x2 integer Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions. Find the optimal solution to the LP relation. Round the value of x2 down to find a feasible mixed-integer solution. Specify upper and lower bounds on the value of the optimal solution to the mixed-integer LP. Find the optimal solution to the mixed-integer LP.

Optimal solution to LP Relaxation x1=3.14 x2=2.60 z=14.08

Round the value of x2 down to find a feasible MILP x1=3.14 x2=2.0 z=2(3.14)+3(2)=6.28+6=12.28 Is it optimal? Why or why not?

An upper bound on the value of the optimal 14.08 Specify upper and lower bounds on the value of the optimal solution to the mixed-integer LP. An upper bound on the value of the optimal 14.08 A lower bound on the value of the optimal 12.28

Find the optimal solution to the mixed-integer LP. From the figure on slide 2, we know that : when x2=3, optimal mixed integer LP solution can be found and the optimal point can be computed by using constraint #1 (4x1+9x2<36) 4x1+9(3)=36 4x1 = 36-27=9 x1=9/4=2.25 The optimal solution is x1=2.25, x2=3.00, Z=13.5

In-class assignment Do problem #2 on page 390 with the following system constraint change. X1, x2>=0 and x2 integer