Linear programming basics: A “feasible solution” to an LP model must do which of the following?
-
ASatisfy the problem constraints
-
BOptimise the objective function
-
CSatisfy all constraints and meet non-negativity restrictions
-
DSatisfy only the non-negativity restrictions
Answer
Correct Answer: Satisfy all constraints and meet non-negativity restrictions
Explanation
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:
List all constraints (equalities/inequalities) and non-negativity for variables.Check whether a candidate vector satisfies each constraint.If all are satisfied, the point is feasible; otherwise, infeasible.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