Question: 1. Given the following all-integer linear program: MAX 3x + 4x2 s.t. 3x1 + x2 5 9 X] + 3x2 5 6 - X1 +

1. Given the following all-integer linear program: MAX 3x + 4x2 s.t. 3x1 + x2 5 9 X] + 3x2 5 6 - X1 + x2 5 2 X1, X220 and integer a Solve the problem as a linear program by following graphical solution procedure and ignoring the integer constraints. Show that the optimal solution to the linear program gives fractional values for both x and x. b. What is the solution obtained by rounding fractions greater than or equal to 1/2 to the next larger number? Show that this solution is not a feasible solution. What is the solution obtained by rounding down all fractions? Is it feasible, and optimal? d. Enumerate all points in the linear programming feasible region in which both x and x are integers, and show that the feasible solution obtained in (c) is not optimal and that in fact the optimal integer is not obtained by any form of rounding. c

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