Graph the constraint inequalities for a linear programming problem shown below. Which feasible region shown is correct? $$\begin{array} { l }
6 x + 4 y \leq 12 \
x \geq 0 , y \geq 0
\end{array}$$

Question

Graph the constraint inequalities for a linear programming problem shown below. Which feasible region shown is correct? $$\begin{array} { l } 
6 x + 4 y \leq 12 \
x \geq 0 , y \geq 0
\end{array}$$

Quizplus · Accepted Answer

The inequality $6x+4y \leq 12$ can be rewritten as $y \leq -\frac{3}{2}x+3$. 
The feasible region should satisfy $x \geq 0$ and $y \geq 0$. 
Option B is the only region that satisfies these conditions and includes the boundary line for $y=-\frac{3}{2}x+3$. Both sides of this boundary line can be tested to find that the feasible region is below the line. Therefore, option B is the correct feasible region.

Graph the Constraint Inequalities for a Linear Programming Problem Shown 6x+4y≤12x≥0,y≥0\begin{array} { l } 6 x + 4 y \leq 12 \\x \geq 0 , y \geq 0\end{array}6x+4y≤12x≥0,y≥0​

Graph the Constraint Inequalities for a Linear Programming Problem Shown $\begin{array} { l } 6 x + 4 y \leq 12 \\x \geq 0 , y \geq 0\end{array}$