Inequalities and linear programming

In linear programming, the region satisfying all the constraints is called the:

• 1 Feasible region
• 2 Objective
• 3 Boundary only
• 4 Optimal point

The optimal value of a linear objective function over a feasible region occurs at a:

• 1 Origin always
• 2 Corner point
• 3 Outside the region
• 4 Midpoint

The inequality 2x + y less than or equal to 6 includes the point:

• 1 (4, 1)
• 2 (3, 3)
• 3 (5, 5)
• 4 (1, 1)

Maximise z = x + y subject to x + y at most 4, x and y at least 0. The maximum value is:

• 1 8
• 2 4
• 3 2
• 4 0

The inequalities x at least 0 and y at least 0 restrict the region to the:

• 1 Second quadrant
• 2 First quadrant
• 3 Fourth quadrant
• 4 Third quadrant

A constraint in a linear programming problem is a:

• 1 Linear inequality
• 2 Matrix
• 3 Quadratic equation
• 4 Constant

An unbounded feasible region means the objective can:

• 1 Be exactly zero only
• 2 Increase without limit in some direction
• 3 Never be positive
• 4 Be negative only