Question

A set of feasible solution to a Linear Programming Problem is .....​

Answer 1

The set of feasible solution to a Linear programming problem is a convex set.

Step-by-step explanation:

Linear program:

• It is widely used in mathematics, and to a lesser extent in business, economics, and for some engineering problems.

• Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing.

• It has proven useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design.

convex set:

1. A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set.
2. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.
3. The branch of mathematics devoted to the study of properties of convex sets and convex functions is called convex analysis.

Answer 2

A set of feasible solutions to the linear programming problem should satisfy the problem constraints and non-negative restrictions.

Step-by-step explanation:

• A feasible solution to a linear programming problem belongs to the feasible region.

• The feasible region is the set of all the points that satisfy the problem's constraints including inequalities, equalities and integer constraints.

• For example, In the following figure, the blue region is the feasible region. All the points in this region are feasible solutions or feasible points which satisfy the given constraints  $(4x+3y\leq 480$ and $2x+3y\leq 360)$.