$1.(10$ points$)$ Nancy Kemp$$s fortieth birthday party promised to be the social event of the year in Richmond.$$ In preparation, Nancy stocked up on the following liquors

$$ Amount stocked

$$ Liquor$($ounces$)$

Bourbon$52$

$$ Brandy$38$

$$ Vodka$64$

$$ Dry vermouth$24$

$$ Sweet vermouth$36$

$$

Bob decides to mix four drinks for the party: Chaunceys, Sweet Italians, bourbon on the rocks, and Russian martinis.$$ A Chauncey consists of $$ bourbon, $$ vodka, $$ brandy, and $$ sweet vermouth.$$ A Sweet Italian contains $$ brandy, $(1)/(2)$ sweet vermouth, and $$ dry vermouth.$$ Bourbon on the rocks contains only bourbon.$$ Finally, a Russian martini consists of $1/3$ dry vermouth and $2/3$ vodka.$$ Each drink contains $4$ fluid ounces.$$ Bob$$s objective is to mix these ingredients in such a way as to make the largest possible number of drinks in advance.$$ Formulate the linear program for this problem and solve.