88556 Minimize \(z=18 x+10 y\) subject to
\(4 x+y \geq 20,2 x+3 y \geq 30 ; x, y \geq 0\)

88557 Maximize \(z=3 x_{1}+4 x_{2}\), if possible, Subject to the constraints
\(\mathrm{x}_{1}-\mathrm{x}_{2} \leq-\mathbf{1},-\mathrm{x}_{1}+\mathrm{x}_{\mathbf{2}} \leq \mathbf{0} ; \mathrm{x}_{\mathbf{1}}, \mathrm{x}_{2} \geq \mathbf{0}\).

88558 Maximize \(\mathrm{z}=7 \mathrm{x}_{1}-3 \mathrm{x}_{2}\), Subject to
\(x_{1}+2 x_{2} \leq \mathbf{2}, 2 x_{1}+4 x_{2} \geq 8, x_{1} \geq 0, x_{2} \geq 0\)

88559 Maximize \(\mathrm{z}=-\mathrm{x}+2 \mathrm{y}\) subject to the constraints
\(x \geq 3, x+y \geq 5, x+2 y \geq 6, y \geq 0\)

88556 Minimize \(z=18 x+10 y\) subject to
\(4 x+y \geq 20,2 x+3 y \geq 30 ; x, y \geq 0\)

88557 Maximize \(z=3 x_{1}+4 x_{2}\), if possible, Subject to the constraints
\(\mathrm{x}_{1}-\mathrm{x}_{2} \leq-\mathbf{1},-\mathrm{x}_{1}+\mathrm{x}_{\mathbf{2}} \leq \mathbf{0} ; \mathrm{x}_{\mathbf{1}}, \mathrm{x}_{2} \geq \mathbf{0}\).

88558 Maximize \(\mathrm{z}=7 \mathrm{x}_{1}-3 \mathrm{x}_{2}\), Subject to
\(x_{1}+2 x_{2} \leq \mathbf{2}, 2 x_{1}+4 x_{2} \geq 8, x_{1} \geq 0, x_{2} \geq 0\)

88559 Maximize \(\mathrm{z}=-\mathrm{x}+2 \mathrm{y}\) subject to the constraints
\(x \geq 3, x+y \geq 5, x+2 y \geq 6, y \geq 0\)

88556 Minimize \(z=18 x+10 y\) subject to
\(4 x+y \geq 20,2 x+3 y \geq 30 ; x, y \geq 0\)

88557 Maximize \(z=3 x_{1}+4 x_{2}\), if possible, Subject to the constraints
\(\mathrm{x}_{1}-\mathrm{x}_{2} \leq-\mathbf{1},-\mathrm{x}_{1}+\mathrm{x}_{\mathbf{2}} \leq \mathbf{0} ; \mathrm{x}_{\mathbf{1}}, \mathrm{x}_{2} \geq \mathbf{0}\).

88558 Maximize \(\mathrm{z}=7 \mathrm{x}_{1}-3 \mathrm{x}_{2}\), Subject to
\(x_{1}+2 x_{2} \leq \mathbf{2}, 2 x_{1}+4 x_{2} \geq 8, x_{1} \geq 0, x_{2} \geq 0\)

88559 Maximize \(\mathrm{z}=-\mathrm{x}+2 \mathrm{y}\) subject to the constraints
\(x \geq 3, x+y \geq 5, x+2 y \geq 6, y \geq 0\)

88556 Minimize \(z=18 x+10 y\) subject to
\(4 x+y \geq 20,2 x+3 y \geq 30 ; x, y \geq 0\)

88557 Maximize \(z=3 x_{1}+4 x_{2}\), if possible, Subject to the constraints
\(\mathrm{x}_{1}-\mathrm{x}_{2} \leq-\mathbf{1},-\mathrm{x}_{1}+\mathrm{x}_{\mathbf{2}} \leq \mathbf{0} ; \mathrm{x}_{\mathbf{1}}, \mathrm{x}_{2} \geq \mathbf{0}\).

88558 Maximize \(\mathrm{z}=7 \mathrm{x}_{1}-3 \mathrm{x}_{2}\), Subject to
\(x_{1}+2 x_{2} \leq \mathbf{2}, 2 x_{1}+4 x_{2} \geq 8, x_{1} \geq 0, x_{2} \geq 0\)

88559 Maximize \(\mathrm{z}=-\mathrm{x}+2 \mathrm{y}\) subject to the constraints
\(x \geq 3, x+y \geq 5, x+2 y \geq 6, y \geq 0\)