Problem $2$ Minimization $(50\%)$:

The owner of a cow feedlot seeks to determine which grains to buy to satisfy minimum nutritional standards and, at the same time, minimize total feed costs.

Each grain contains different amounts of four nutritional ingredients: A$,$ B$,$ C$,$ and D$.$ Here are the ingredient contents of each grain, in ounces per pound of grain:

$\backslash$table$[[$Cow Feed$],[$Nutritional Ingredient $($Per pound of grain$),$Grain $x,$Grain $Y,$Grain Z$],[$A$,3$ oz$,2$ oz$,4$ oz$],[$B$,2$ oz$,3$ oz$,1$ oz$],[$C$,1$ oz$,0$ oz$,2$ oz$],[$D$,6$ oz$,8$ oz$,40$ oz$]]$

The cost per pound of grains $x,Y,$ and $Z$ is $$0\mathrm{.}03,$$$0\mathrm{.}04,$ and $$0\mathrm{.}025,$ respectively. The minimum requirement per cow per month is $64$ ounces of ingredient $A,80$ ounces of ingredient B$,16$ ounces of ingredient C$,$ and $128$ ounces of ingredient D$.$

The feedlot faces one additional restriction: it can only obtain $500$ pounds of Grain $Z$ per month from its supplier. Because there are a constant number of $100$ cows at the feedlot at any given time, this constraint limits the amount of Grain $Z$ for use in the feed of each cow to no more than $5$ pounds per month per cow.

What are the grains to purchase per cow per month? What is the cost to feed per cow per month?

Submit your Excel file showing the formula of the linear program along with its solutions.