Question

1. Non-negativity is always present in a linear programming problem.

A) True

B) False

2. In all linear programming problems, the maximization or minimization of some quantity is the objective.

A) True

B) False

3. All linear programming problems have at least one feasible solution.

A) True

B) False

4. The point (0,0) is always part of the feasible region.

A) True

B) False

5. The optimal solution for a linear programming problem occurs when the objective function intersects with at least one of the corner points.

A) True

B) False

Answer 1

1. TRUE. Even if non-negativity is not present, we can change it to non-negativity. For example if a condition is x1<=0, we can replace x1 by -x1 and the condition becomes, -x1>=0

2. TRUE. Linear programming is done to maximize or minimize an objective.

3. FALSE. There are infeasible linear programming problems. For example,

Max (x1)+2(x2) subject to x1+x2<=-1, x1-x2<=2; x1,x2>=0.

Then x1,x2>=0 implies x1+x2>=0. Thus x1+x2<=-1 can never be satisfied. Hence, this program is infeasible.

4. FALSE. Consider the following:

Min (x1)+2(x2) subject to x1+x2>=3; x1,x2>=0.

Note that (0,0) is not included in the feasible region as x1+x2 at (0,0) is 0+0 = 0<3. Thus, (0,0) doesn't satisfy the constrain,

5. There is an ambiguity, as the objective function isn't a line and hence can't INTERSECT a corner point. Also it's not always true that a corner point is the optimal solution. For example, in an unbounded LPP, the corner point is not an optimal solution. Hence, this is FALSE.