\left\{ \begin{array} { c } { 3 x + 2 y \leq 5,000 } \\ { x + 0.5 y \leq 1,600 } \\ { 4 x + 5 y \leq 9,600 } \\ { 0 \leq y \leq 2,000 } \\ { x \geq 0 } \end{array} \right.
Solve for x
\left\{\begin{matrix}x\in \begin{bmatrix}0,-\frac{y}{2}+1600\end{bmatrix}\text{, }&y\geq 0\text{ and }y\leq 400\\x\in \begin{bmatrix}0,\frac{5000-2y}{3}\end{bmatrix}\text{, }&y>400\text{ and }y<\frac{8800}{7}\\x\in \begin{bmatrix}0,-\frac{5y}{4}+2400\end{bmatrix}\text{, }&y\geq \frac{8800}{7}\text{ and }y\leq 1920\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y\in \begin{bmatrix}0,3200-2x\end{bmatrix}\text{, }&x\geq 1400\text{ and }x\leq 1600\\y\in \begin{bmatrix}0,-\frac{3x}{2}+2500\end{bmatrix}\text{, }&x>\frac{5800}{7}\text{ and }x<1400\\y\in \begin{bmatrix}0,-\frac{4x}{5}+1920\end{bmatrix}\text{, }&x\geq 0\text{ and }x\leq \frac{5800}{7}\end{matrix}\right.
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