# An optimal solution to a linear programming problem must lie?

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## Problem:

Can anyone help with right solution?

An optimal solution to a linear programming problem MUST lie?

A. somewhere outside of the feasible region.
B. somewhere on the line between two corner points.
C. at the intersection of at least two constraints.
D. somewhere in the interior of the feasible region.

## Solution:

The correct answer is: at the intersection of at least two constraints.

Definition:
A linear programming problem (LP) is an optimization problem for which:
1. We attempt to maximize (or minimize) a linear function of the decision variables. (objective function)
2. The values of the decision variables must satisfy a set of constraints, each of which must be a linear inequality or linear equality.
3. A sign restriction on each variable.
For each variable xi the sign restriction can either say
(a) xi ≥ 0,
(b) xi ≤ 0,
(c) xi unrestricted (urs)

## Solution:

The Correct Answer of this question is
C. at the intersection of at least two constraints.

### Explanation:

Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

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