Question: If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding up the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem.

Hint: Solve a small size problem, such as below, and simulate the given scenario.

Max 2.4x + 5.2y

Subject to

1.4x + 3.6y <= 8

2.1 x - 3y <= 21

x, y > 0

A) always, non-optimal B) always, optimal C) sometimes, optimal D) never, non-optimal

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