**Duality in Linear Programming: Understanding Feasible Solutions**In the field of linear programming, understanding the relationship between primal and dual problems is crucial. This exercise demonstrates an important concept in duality theory. ### Problem Statement:*If a feasible solution to the primal minimization problem is 85, then 90 could be a feasible solution to the dual maximization problem.*### Options:- **True**- **False** (selected)### Explanation:This statement tests the knowledge of the relationship between the solutions of primal and dual problems. In linear programming, the value of the objective function for a feasible solution to the primal problem serves as a lower bound for the dual problem (for a minimization primal and maximization dual). The optimal solution of the dual problem gives an upper bound to the primal minimization problem. Consequently, if 85 is a feasible solution to the primal problem, any solution greater than 85 cannot be feasible for the dual problem. Therefore, the correct answer here is "False", indicating the understanding that 90 cannot be a feasible solution to the dual maximization problem if 85 is a feasible solution to the primal minimization problem.

A feasible solution is a set of values for the decision variables that satisfies all of the…

Answered: If a feasible solution to the primal…

If a feasible solution to the primal minimization problem is 85, then 90 could be a feasible solution to the dual maximization problem. Select one: O True False 4

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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Concept explainers

Duality

Duality is a linear programming (LP) concept which states that it is possible to interpret every LP problem using two distinct methods, but they will have similar solutions. That means any LP problem can be mentioned in another equivalent form based on identical data.

Question

**Duality in Linear Programming: Understanding Feasible Solutions**

In the field of linear programming, understanding the relationship between primal and dual problems is crucial. This exercise demonstrates an important concept in duality theory.

### Problem Statement:

*If a feasible solution to the primal minimization problem is 85, then 90 could be a feasible solution to the dual maximization problem.*

### Options:

- **True**
- **False** (selected)

### Explanation:

This statement tests the knowledge of the relationship between the solutions of primal and dual problems. In linear programming, the value of the objective function for a feasible solution to the primal problem serves as a lower bound for the dual problem (for a minimization primal and maximization dual). The optimal solution of the dual problem gives an upper bound to the primal minimization problem. Consequently, if 85 is a feasible solution to the primal problem, any solution greater than 85 cannot be feasible for the dual problem. Therefore, the correct answer here is "False", indicating the understanding that 90 cannot be a feasible solution to the dual maximization problem if 85 is a feasible solution to the primal minimization problem.

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