CheeseCo processes dairy and non$-$dairy milks to make cheese products. Milk can be purchased for

$$20/$vat$,$ and must first be pasteurized, which costs $$5$ and uses $0\mathrm{.}5$ hours of labor per vat. The pasteurized

milk can then be processed to produce cheese in two different ways. Method $1$ yields $2$ wheels of cheese,

$9$ small blocks of cheese, and $30$ ounces of waste material. Method $1$ costs $$3/$vat of milk, and takes $1\mathrm{.}2$

hours of labor. Method $2$ produces $3$ wheels of cheese, $4$ small blocks of cheese, and $40$ ounces of waste

material. Method $2$ costs $$4/$vat of milk, and takes $2$ hours of labor. A cup of specialty cheese spread can

be made using $12$ ounces of waste material at a cost of $$3$ per cup, and using $0\mathrm{.}5$ hours of labor. The sales

price and maximum sales amount of each product are given in the table below. CheeseCo has at most $300$

hours of labor available. $($You may assume that excess cheeses or waste material, if any cannot be sold due

to sales limits$,$ may be discarded at no cost$.)$

Products $($p in P $)$ Small blocks Wheels Waste Material Specialty Spread

Sales Price $($Sp$)$ $$3/$block $$10/$wheel $$1/$oz $$20/$cup

Maximum Can Sell $($Mp$)500$ blocks $250$ wheels $3000$ oz $400$ cups

$2-1$ Problem Formulate a linear program that can help CheeseCo determine how to maximize its profit.