1. Integer LP In-class Prob
Consider the following mixed-integer LP.
Max z = 2x1 + 3x2
s.t x1 + 9x2 < 36
7x1 + 5x2 < 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.

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

3. 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?

4. 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
A lower bound on the value of the optimal

5. 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

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