\text { Minimize } & \mathrm{z}=5 \mathrm{x}_{1}+6 \mathrm{x}_{2}+7 \mathrm{x}_{3} \\ \text { subject to } & 3 \mathrm{x}_{1}+2 \mathrm{x}_{2}+3 \mathrm{x}_{3} \quad \geq 10 \\ & 4 \mathrm{x}_{1}+3 \m...\text { Minimize } & \mathrm{z}=5 \mathrm{x}_{1}+6 \mathrm{x}_{2}+7 \mathrm{x}_{3} \\ \text { subject to } & 3 \mathrm{x}_{1}+2 \mathrm{x}_{2}+3 \mathrm{x}_{3} \quad \geq 10 \\ & 4 \mathrm{x}_{1}+3 \mathrm{x}_{2}+5 \mathrm{x}_{3} \geq 12 \\ &\mathrm{x}_{1}, \mathrm{x}_{2}, \mathrm{x}_{3} \geq & 0 If Food A costs $3 per unit, Food B costs $2 per unit and Food C costs $3 per unit, how many units of each food should be purchased to keep costs at a minimum?
