What is a linear programming problem? Discuss the scope and

Question

What is a linear programming problem? Discuss the scope and role of linear programming in solving management problems.

03 Mar 2025

Answer :

Word Count : 584

A Linear Programming Problem (LPP) is a mathematical technique used in operations research to optimize a given objective function, subject to a set of linear constraints. The objective function usually represents cost minimization or profit maximization, while the constraints represent resource limitations such as labor, materials, and time. LPP is expressed in the form:

1. Objective Function: A linear function to be maximized or minimized, such as:
\[
Z = c_1x_1 + c_2x_2 + \dots + c_nx_n
\]
where \( Z \) is the objective value, \( c_i \) are coefficients, and \( x_i \) are decision variables.

2. Constraints: Linear inequalities or equalities that restrict the values of decision variables:
\[
a_{11}x_1 + a_{12}x_2 + \dots + a_{1n}x_n \leq b_1
\]
\[
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