Optimal cost An animal shelter mixes two brands
of dry dog food. Brand $\mathrm{X}$ costs $\$ 25$ per bag and contains
two units of nutrient $\mathrm{A},$ two units of nutrient $\mathrm{B},$ and two
units of nutrient $\mathrm{C}$ . Brand $\mathrm{Y}$ costs $\$ 20$ per bag and
contains one unit of nutrient $\mathrm{A}$ , nine units of nutrient $\mathrm{B}$ ,
and three units of nutrient $\mathrm{C} .$ The minimum required
amounts of nutrients $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$ are 12 units, 36 units,
and 24 units, respectively. What is the optimal number
of bags of each brand that should be mixed? What is the
optimal cost?