Question

Unboundedness is usually a sign that the LP problem.
A) has finite multiple solutions.
B) Is degenerate.
C) contains too many redundant constraints.
D) has been formulated improperly.
E) none of the above.

Answer 1

Hint:
Here we need to choose the correct option which will complete the given statement. We will first explain the meaning of the LP. Then we will describe the unbounded solution or unboundedness in the LP and then we will choose the correct option accordingly. LP can be defined as the problem of minimizing or maximizing a linear function which is subjected to linear constraints. The constraints may be inequalities or equalities.

Complete step by step solution:
We know that LP stands for Linear Programming. Linear programming is defined as the method for achieving the best outcome in a mathematical model where the requirements are generally represented by linear relationships. Linear programming is also known as Linear Optimization.
An unbounded solution in a linear programming problem is considered as a situation in which the objective function is not finite. In other words, a linear programming problem is said to have an unbounded solution if the solution of the linear programming can be made infinitely large without violating any of its constraints in the problem.
So we can say that unboundedness is a sign that the linear programming problem has infinite solutions.

Hence, the correct option is option A.

Note:
We can solve linear programming either by simplex method or by graphical method. In the Simplex Method, an unbounded solution is considered only when there are only negative values of the replacement ratio. This means that the replacement ratio values are either negative or infinite. In this case, there will be no outgoing variable. In the graphical method, we can find the solutions by obtaining a feasible region.