$4$ SnakeBoocha

Tom$($from "The Office"$)$ is creating a new line of beverages: Snakeboocha $1($S$1),$ Snakeboocha $2($S$2),$

and Snakeboocha $3($S$3).$ Ron has helped him create two processes that can be run in a fermenting

machine for making these products. Running process A for an hour consumes $50$ ounces of tea and

$16$ pounds of sugar, and yields $3$ gallons of $S1,2$ gallons of S $2,$ and $75$ ounces of tea sludge. Running

process B for an hour consumes $30$ ounces of tea, $10$ pounds of sugar, and $1$ gallon of S $1$ and produces $2$

gallons of S$2,3$ gallons of S$3,$ and $40$ ounces of tea sludge. Tom has one fermenting machine which he

can run for a total of $60$ hours per week. Tom can buy sugar for $$2$ per pound, tea for $$1\mathrm{.}5$ per ounce,

and must pay $$0\mathrm{.}25$ per ounce to dispose of tea sludge. Tom can sell each beverage $(S1,S2,$ and S $3)$ by

the gallon and also sells "Value packs" which consist of $3$ gallons of S$1,2$ gallons of S$2,$ and $1$ gallon

of S$3.$ The selling price and maximum that can be sold of each product per week is listed in the table

below:

$4-1$ Problem Formulate a an optimization model to help Tom maximize his weekly profit. $($You do

not have to implement this in Julia$/$JuMP$.)$