Question

Suppose that the following constraints have been provided for a linear programming model with decision variables x₁ and x2. - X1 + 3x25 30

-3X₁+ 3X₂≤ 30
and
-3X₁+X₂≤30
Demonstrate graphically that the feasible region is unbounded.
If the objective is to maximize Z = - X₁+ X2, does the model have an optimal solution? If so, find it. If not, explain why not.

Answer 1

To demonstrate graphically that the feasible region is unbounded, plot the given constraints on a graph. To determine if the model has an optimal solution, maximize the objective function within the feasible region.

Step-by-step explanation:

To demonstrate graphically that the feasible region is unbounded, we will plot the given constraints on a graph. The first constraint, -x1 + 3x2 ≤ 30, can be rewritten as 3x2 ≥ x1 - 30. The second constraint, -3x1 + x2 ≤ 30, can be rewritten as x2 ≥ 3x1 - 30. Plotting these inequalities on a graph will show that the feasible region is unbounded.

To determine if the model has an optimal solution, we will maximize the objective function, Z = -x1 + x2, within the feasible region. Since the feasible region is unbounded, the model does not have an optimal solution.