Question

For a linear programming equation, convex set of equations is included in region of
A. Feasible solutions
B. Disposed solutions
C. Profit solutions
D. Loss solutions

Answer 1

Hint:For, the linear programming problem to have a unique solution, we take into consideration
One equation, represents a objective function of $x$ and $y$, i.e. $z = ax + by$ and the two inequalities, represents the constraints like $mx + ny \geqslant c$ or $px + qy \leqslant r$.

Complete step-by-step answer:
Step by step solution:
For defining a linear programming problem to have a unique solution.
The solution must exist at the intersection of two or more constraints and should be confined by using all alterations.
Then, the problem becomes convex means there are no dents or indentations in the curve or polygon and has a single optimum (maximum or minimum) solution, which is possible when constraints are satisfied by the set of points that satisfy inequalities, thus feasible region is required.
Therefore, the convex set of equations is included in the feasible region.

So, the correct answer is “Option A”.

Note:A feasible region is defined by the set of points which satisfy a system of constraints i.e., inequalities. The region satisfies all restrictions imposed by linear programming scenario. The concept is an optimization technique.
The convex set is a set of points in a plane that is said to be convex, the line segment joining any two points in the set, completely lies in the set.
A bounded feasible region will have both a maximum value and minimum value for the objective function. It is bounded if it can be enclosed in any shape.