Question

Which of the following linear programming problems with the given constraints gives an unbounded feasible region

• A. A linear programming problem with the constraints x ≥ 0 y ≥ 0, x + 2y ≤ 8, 3x+2y ≤ 1
• B. A linear programming problem with the constraints x ≥ 0 y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10
• C. A linear programming problem with the constraints x ≥ 0 y ≥ 0, 2x+y ≥ 3, x+2y ≥ 6
• D. None of the options given

Answer 1

The correct option is C

A linear programming problem with the constraints x ≥ 0 y ≥ 0, 2x+y ≥ 3, x+2y ≥ 6

We will go through the options and see which among them represent a linear programming problem with unbounded feasible region.

A linear programming problem with the constraints x ≥ 0 y ≥ 0, x + 2y ≤ 8, 3x+2y ≤ 12:

When we draw the common region for these constraints on graph we get the following shaded region

This is a bounded feasible region as it is bounded by four straight lines

A linear programming problem with the constraints x ≥ 0 y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10:

When we draw the common region for these constraints on graph we get the following shaded region

A linear programming problem with the constraints x ≥ 0 y ≥ 0, 2x+y ≥ 3, x+2y ≥ 6:

When we draw the common region for these constraints on graph we get the following shaded region

This region is not bounded on the upper side. We call this unbounded feasible region. Other two feasible regions are bounded feasible regions