Question

Minimization of objective function in lpp means

Answer 1

Answer:

The function to be optimized in linear programming is called the objective function. This usually refers to profit maximization or cost minimization. In linear programming problems, constraints are given by inequalities (called inequality constraints). ... Graph the inequality constraints, and define the feasible region.

Answer 2

Answer:

Minimization of the objective function in LPP means among the allowable decisions, least value is chosen.

Step-by-step explanation:

Consider the problem as follows:

Min $c_1x_1+c_2x_2+.\ . \ .\ + c_nx_n$ _____ (A)

Subject to $a_{11}x_1+a_{12}x_2+.\ .\ .\ +a_{1n}x_n=b_1$ _____ (1)

                 $a_{21}x_1+a_{22}x_2+.\ .\ .\ +a_{2n}x_n=b_2$ _____ (2)

                  $\vdots$               $\vdots$                     $\vdots$             $\vdots$

                $a_{m1}x_1+a_{m2}x_2+.\ .\ .\ +a_{mn}x_n=b_m$ _____ (m)

                                             $x_1,x_2,.\ .\ .\ x_n\geq 0$ ______ (B)

Here,

Equation (A) is called objective function.

Equation (1), (2), . . . (m) are called constraints.

Inequality (B) is called non- negativity restrictions.

$c_1, c_2, . . . c_n$ is called price or cost.

(I) The values of $x_1,x_2,...,x_n$ which satisfies equations from (1) to (m) gives the solution for LPP.

(II) A solution $(x_1,x_2,...,x_n)$ which satisfies (B) is called feasible solution.

(III) A feasible solution which minimize the objective function in a minimization problem is called optimal solution.

Therefore, the least value of objective function gives maximum profit.

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