# Use LP relaxation to solve Mix Integer programming problem

Consider the following all-integer linear program:

Max 2x1+3x2

s.t.

4x1+9x2<36

7x1+5x2<35

1x1+2x2<10

X1,x2>0 and x1 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 x1 down to find a feasible mixed-integer solutions. Is this solution optimal? Why or why not?

c. Find the optimal solution for the mixed-integer linear program.

Â© BrainMass Inc. brainmass.com December 24, 2021, 10:07 pm ad1c9bdddfhttps://brainmass.com/math/linear-programming/use-lp-relaxation-to-solve-mix-integer-programming-problem-444256

#### Solution Preview

An LP relaxation problem is formulated for the Mix Integer programming problem.

The LP relaxation problem is ...

#### Solution Summary

An LP relaxation problem is formulated for the Mix Integer programming problem.

The LP relaxation problem is solved using graphical method and an upper bound is find for the original Mix Integer programming problem.

Additional LP relaxation problems are formulated and solved to find a feasible and optimal solution for the original Mix Integer programming problem.