A problem often of concern to managers in processing industries is blending. The Nutmeg Corporation, from Problem $15,$ is considering a new product it intends to sell to active and health$-$concerned adults. This new product will be a $4-$ounce package of nuts that conforms to specific heath requirements. First, the $4-$ounce package can contain no more than $720$ calories. It must deliver at least $20$ grams of protein. Finally, the package must provide at least $15$ percent of the adult daily requirement $($ADR$)$ of calcium and $20$ percent of the ADR of iron. Nutmeg would like to use only almonds, walnuts, and peanuts in this new product. The following table provides nutritional data on each of these ingredients as well as their cost to Nutmeg.

Ingredients

Calories per Ounce

Grams of Protein per Ounce

Percent ADR of Calcium per Ounce

Percent ADR of Iron per Ounce

Cost per Ounce

Almonds

$180$

$6$

$8\%$

$6\%$

$$0\mathrm{.}28$

Walnuts

$190$

$4$

$2\%$

$6\%$

$$0\mathrm{.}38$

Peanuts

$170$

$7$

$0\%$

$4\%$

$$0\mathrm{.}12$

a$.$Use linear programming to find the cost$-$minimizing number of ounces of each ingredient that Nutmeg should use in each $4-$ounce package. What is the per$-$package cost of raw materials?