# Integer programming problems: Optimal solution

1. Integer Programming Problem

Consider the following integer linear programming problem

Max Z=3x1+2x2

Subject to:

3x1+5x2<=30

5X1+2x2<=28

x1<=8

x1,x2>=0 and integer

The solution to the Linear programming relaxation is: x1 = 5.714, x2= 2.571.

What is the Z value for the optimal solution under integer constraints?

a) 18 b) 19 c) 20 d) 24

2. Integer Programming Problem

Max Z=x1+6x2

Subject to

17x1+8x2<=136

3x1+4x2<=36

x1,x2>=0 and integer

Find the Z value of the optimal solution

a) 50 b) 52 c) 54 d) 56

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