91Ó°ÊÓ

Maximize \(\quad P=-x+8 y\) subject to \(\quad-3 x+4 y \leq 10\) \(-x+4 y \leq 14\) \(3 x+2 y \leq 21\) \(3 x+y \leq 18\)

$$ \begin{array}{rr} \text { Maximize } & P=-4 x+8 y \\ \text { subject to } & x+3 y \leq 57 \\ & 7 x+4 y \leq 110 \\ & -x+5 y \leq 40 \end{array} $$

\(\begin{array}{rr}\text { Maximize } & P=-3 x+4 y \\ \text { subject to } & 3 x-2 y \leq 15 \\ x+y \leq 10 \\ -x+4 y \leq 15 \\ -2 x+y \leq 2\end{array}\)

$$ \begin{array}{rr} \text { Maximize } \quad P=5 x+4 y \\ \text { subject to } \quad x-2 y \leq 2 \\ 3 x-4 y \leq 8 \\ 5 x+6 y \leq 45 \\ x+3 y \leq 18 \end{array} $$

$$ \begin{aligned} \text { Maximize } & P=2 x+y \\ \text { subject to } & x+4 y \leq 24 \\ & x+y \leq 9 \\ & x-y \leq 3 \\ & x-2 y \leq 2 \end{aligned} $$

$$ \begin{array}{rr} \text { Minimize } & P=3 y-4 x \\ \text { subject to } & x+4 y \leq 60 \\ & 2 x+y \leq 22 \\ & -x+y \geq 7 \end{array} $$

$$ \begin{array}{rr} \text { Maximize } & P=-3 x+4 y \\ \text { subject to } & 3 x-4 y \leq 12 \\ 5 x+4 y \leq 36 \\ -x+3 y \leq 8 \\ -3 x+y \leq 0 . \end{array} $$

$$ \begin{aligned} \text { Minimize } \quad P=2 x-3 y+z &-2 w \\ \text { subject to } \quad 4 x+2 y+3 w & \geq 5 \\ x+2 z-5 w & \leq 10 \\ x-5 y-z+w & \geq 15 \\ -2 x-3 y+4 z+2 w & \leq 55 . \end{aligned} $$

$$ \begin{aligned} \text { Maximize } & P=4 y-3 x \\ \text { subject to } & x-2 y \leq 0 \\ x-y \leq 2 \\ x+2 y \leq 14 \\ -x+2 y \leq 6 \\ -3 x+2 y \leq 2 \end{aligned} $$

$$ \begin{aligned} \text { Maximize } \quad P=3 x+4 y+5 z \\ \text { subject to } \quad 5 x+4 y+8 z \leq 40 \\ 3 x+2 y+12 z \leq 30 \\ y \leq 8 \end{aligned} $$