Given the Following All-Integer Linear Program: ​

question 9

Essay

Given the following all-integer linear program: ​
a.​
Solve the problem as a linear program ignoring the integer constraints.Show that the optimal solution to the linear program gives fractional values for both x₁ and x₂.
b.​
What solution is 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.
c.What is the solution obtained by rounding down all fractions? Is it feasible?
d.​
​
Enumerate all points in the linear programming feasible region in which both x₁ and x₂ are integers,and show that the feasible solution obtained in part (c)is not optimal and that in fact the optimal integer is not obtained by any form of rounding.

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