Question

What is the objective function in linear programming problems?

Answer 1

Hint: We first explain the concept of linear programming problems and the use of objective function in linear programming problems. The use of objective function and its algebraic form is also discussed.

Complete step-by-step answer:
A linear programming problem may be defined as the problem of maximizing or minimizing a linear subject to a system of linear constraints. The constraints may be equalities or inequalities.
The objective function of linear programming problems is defined by two variables’ function as $ f\left( x,y \right)=ax+by+c $ . We try to find the optimised value of the function. It can be both maximum and minimum values.
The objective function in a mathematical optimization problem is the real-valued function whose value is to be either minimized or maximized over the set of feasible alternatives.
We can also define the function as a third variable where $ z=ax+by+c $ .

Note: The condition for the objective function is that all the inputs have to be real-valued and it has to be in the limits or boundaries of the given variables. In many cases the function is defined in single form of summation as $ z=\sum\limits_{i=1}^{n}{{{c}_{i}}{{X}_{i}}} $ . It is the most general form where $ {{c}_{i}} $ denotes the coefficients of the variables $ {{X}_{i}} $ .