Transcript Slide 1

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
1.
Graph the constraints for this problem. Indicate on your graph all
feasible mixed-integer solutions.
2.
Find the optimal solution to the LP relation.
3.
Round the value of x2 down to find a feasible mixed-integer
solution.
4.
5.
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?
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 mixedinteger 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