Hint: You can visualize the case $n=2$ to understant

Question $3.(20$ points$)$: The bartender of your local pub asks you to assist him in finding the combination

of mixed drinks to maximize his revenue. He has the following bottles available:

$1$ quart $(32$ oz $.)$ Old Cambridge $($a fine whiskey$)$

$1$ quart Joy Juice $($another fine whiskey$)$

$1$ quart Ma's Wicked Vermouth

$2$ quarts Gil$-$boy's Gin

Since he is new to the business, his knowledge is limited to the following drinks:

Whiskey Sour. Each serving uses $2$ oz $.$ whiskey and sells for $$1.$

Manhattan. Each serving uses $2$ oz$.$ whiskey and $1$ oz$.$ vermouth, and sells for $$2.$

Martini. Each serving uses $2$ oz$.$ gin and $1$ oz $.$ vermouth, and sells for $$2.$

Pub Special. Each serving uses $2$ oz$.$ gin and $2$ oz$.$ whiskey, and sells for $$3.$

Answer the following questions:

First, formulate an LP model to maximize the bar's profit. Ignore the fact that the numbers of servings

have to be integers.

Second, if the problem is not canonical, convert it into a standard form, and you will see the resulting

problem is canonical.

Next, solve the LP using the simplex method.

Finally, convert the solution to the solution of the original problem and interpret the result.