Linear Programming

$$ \begin{aligned} & \text { Maximize } \mathrm{z}=25 x+18 y \\ & \text { subject to } 20 x+15 y \leq 640 \\ &\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, 5 x+8 y \geq 500 \\ &\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, x, y \geq 0 \end{aligned} $$

Maximize $z=25 x+18 y$

$$ \begin{aligned} \text { subject to } 20 x+15 y & \leq 640 \\ 5 x+8 y & \leq 500 \\ x, y & \geq 0 \end{aligned} $$

$$ \begin{array}{r} \text { Maximize } z=25 x+18 y \\ \text { subject to } 20 x+5 y \leq 8 \\ 5 x+8 y \leq 10 \\ x, y \geq 0 \end{array} $$

$$ \begin{aligned} & \text { Maximize } \mathrm{z}=25 x+18 y \\ & \text { subject to } 4 x+3 y \leq 128 \\ & \qquad \begin{array}{r} 5 x+8 y \geq 500 \\ x, y \geq 0 \end{array} \end{aligned} $$