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Integer programming problems: Optimal solution

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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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