Question

LP Theory states that the optimal solution to any problem will lie at
A. The origin.
B. A corner point of the feasible region
C. The highest point of the feasible region.
D. The lowest point in the feasible region.

Answer 1

Linear Programming Problem: A linear programming problem (LPP) is the one in which we are concerned with finding the optimal value (maximum or minimum) of a linear function of several variables (called objective function) subject to the constraints that the variables are non-negative and satisfy a set of linear inequalities (called linear constraints).

Complete step-by-step answer:
In the LP problem, we plot the constraints given to us and obtain a feasible region which may be bounded or unbounded.
To find the optimal solution, we check the corner points of the region obtained and find the value of objective function at each of the corner points. The optimal solution to the objective function lies at any of the corner points of the feasible region which gives the maximum or minimum value of the objective function according as the problem is maximization or minimization problem.
Thus, the optimal solution to any problem will lie at a corner point of the feasible region.
Hence, option B is correct.

Note: Any point in the feasible region that gives the optimal value (maximum or minimum) of the objective function is called an optimal solution. In most cases, the optimal solution occurs at the corner points (vertex) of the feasible region.
In LP problems the optimal solution required may occur at more than one corner point and also at line joining any two corner points.