To convert the given inequality into an equation, follow these steps:
1. Understand the inequality:
[tex]\[ 8 x_1 + 3 x_2 + 6 x_3 \leq 181 \][/tex]
2. Introduce a slack variable:
- A slack variable is a non-negative variable that we add to convert an inequality into an equation. It accounts for the difference between the left side and the right side of the inequality.
3. Form the equation:
- Add a slack variable [tex]\( s_1 \)[/tex] to the inequality where [tex]\( s_1 \)[/tex] is non-negative (i.e., [tex]\( s_1 \geq 0 \)[/tex]) to turn the inequality into an equation:
[tex]\[ 8 x_1 + 3 x_2 + 6 x_3 + s_1 = 181 \][/tex]
4. Choose the correct corresponding equation:
- This step involves matching our derived equation with the options provided.
Based on the above steps, the correct corresponding equation is:
[tex]\[ 8 x_1 + 3 x_2 + 6 x_3 + s_1 = 181 \][/tex]
Thus, the correct choice is:
A. [tex]\( 8 x_1 + 3 x_2 + 6 x_3 + s_1 = 181 \)[/tex]
