Linear programming basics: A “feasible solution” to an LP model must do which of the following?

Introduction / Context:
In linear programming (LP), we distinguish between feasible solutions and optimal solutions. Many candidate solutions can be feasible; only one (or more) is optimal.

Given Data / Assumptions:

• Standard LP with linear objective and linear constraints.
• Decision variables are subject to non-negativity (x ≥ 0).
• Feasibility precedes optimality in the solution process.

Concept / Approach:
A feasible solution is any assignment of decision variables that satisfies every constraint simultaneously, including non-negativity, regardless of the objective value. Optimality is evaluated only among feasible solutions.

Step-by-Step Solution:

Verification / Alternative check:
Graphical LP for two variables shows the feasible region (intersection of half-planes). Any point within/on the boundary meets constraints and non-negativity.

Why Other Options Are Wrong:
(a) ignores non-negativity; (b) confuses feasibility with optimality; (d) ignores structural constraints.

Common Pitfalls:
Believing the best objective value at an infeasible point is meaningful; it is not.

Final Answer:

Satisfy all constraints and meet non-negativity restrictions