nutrients to be found on the whole of each feed type. Finally, constraint set $($vi$)$ implies the non$-$negativity of each ingredient amount to be used in each feed type.

$(35$p$)$ Now, consider an instance of the feed mix problem, in which an agricultural mill manufactures feed for cattle, sheep, and chickens, by mixing the following raw ingredients: corn, limestone$,$ soybeans, and fish meal. These ingredients contain the following nutrients: vitamins, protein, calcium, and crude fat. The contents of the nutrients in standard units for each kilogram of the ingredients are summarized in the following table. We also have information on the unit cost and available stock levels of ingredients.

$\backslash$table$[[,$Nutrient$],[$Ingredient$,$Vitamins,Protein,Calcium,Crude Fat$],[$Corn$,8,10,6,8],[$Limestone$,6,5,10,6],[$Soybeans$,10,12,6,6],[$Fish meal,$4,18,6,9]]$

$\backslash$table$[[$Unit Cost $(\frac{\text{\$}}{k}g)$