$3.(20)$ Aidan, an aerospace engineering major functioning purely on caffeine, has the following

preferences over Americanos $($A$)$ and Macchiatos $($M$)$:

U $($A$,$ M $)=$ A $+2$M

The price of an americano is $$4$ and the price of a macchiato is $$6.$ Aidan has $$12$ to spend on

his daily caffeine fix.

$($a$)(10)$ How many americanos will Aidan buy? How many macciatos will Aidan buy? Label

your answers A$$ and M $$ and draw a box around them.

$($b$)(10)$ Show this solution graphically $($label A$$ and M $,$ the IC at the optimum, the budget

line, and all axes and other relevant points$).$

Page $1$ of $1$