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# Integer programming problem

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1. Consider the following integer linear programming problem.
Max Z = 3x1 + 2x2
Subject to: 3x1 + 5x2 <= 30
4x1 + 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 optimal solution to the integer linear programming problem? State the value of the objective function Z = x or x.x

2. Consider a capital budgeting example with 5 projects from which to select. Let x1 = 1 if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Conditions are independent. Projects cost \$100, \$200, \$150, \$75, and \$300 respectively. The budget is \$450. Write the appropriate constraint for the following condition. If project 1 is chosen, project 5 must not be chosen.
Put your response in the form xi + xj <=> k (fill in the correct i,j,k and <=>)

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