Convert the constraints into linear equations by using slack variables.
-Maximize $z=3 x_{1}+5 x_{2}$
Subject to: $3 x_{1}+3 x_{2} \leq 30$
$$x_{1}+4 x_{2} \leq 40$$
$$x_{1} \geq 0, x_{2} \geq 0$$
A) $3 x_{1}+3 x_{2}=s 1+30$
$\mathrm{x}_{1}+4 \mathrm{x}_{2}=\mathrm{s}_{2}+40$
B) $3 x_{1}+3 x_{2}+s_{1}=30$
$\mathrm{x}_{1}+4 \mathrm{x}_{2}+\mathrm{s}_{2}=40$
C) $3 x_{1}+3 x_{2}+s_{1} \geq 30$
$\mathrm{x}_{1}+4 \mathrm{x}_{2}+\mathrm{s}_{2} \geq 40$
D) $3 x_{1}+3 x_{2}+s_{1} \leq 30$
$\mathrm{x}_{1}+4 \mathrm{x}_{2}+\mathrm{s}_{2} \leq 40$

Question

Quizplus · Accepted Answer

The constraints are converted into linear equations by adding slack variables to make them equalities. The slack variables are non-negative and represent the amount by which the left-hand side of the inequality can be increased to make it equal to the right-hand side. In this case, the slack variables are $s_1$ and $s_2$. The correct answer is B because it adds slack variables to both constraints and makes them equalities.

Convert the Constraints into Linear Equations by Using Slack Variables z=3x1+5x2z=3 x_{1}+5 x_{2}z=3x1​+5x2​

Convert the Constraints into Linear Equations by Using Slack Variables $z=3 x_{1}+5 x_{2}$