Problem $3.$ Tatte Like Latte Part One $(10$ points$)$

You have $$D$ to spend on pastries at Tatte. In the bakery display, you see exactly one of each item $-$

each has a price listed next to it$,$ and you've personally assigned a rating of $1-10$ as well. You want

to spend your money in an optimal way, i$.$e$.,$ you want to maximize the sum of ratings on your

items without going over $$D.$

Here are the items you can buy, along with their prices and your individual ratings:

$($a$)$ What would an optimal solution be if you have $$10$ to spend? What is the value of that solution

$($i$.$e$.,$ what is the sum of all the ratings$)?$

Solution:

$($b$)$ Going by ratings $($largest to smallest$),$ what would a Greedy solution be assuming you have

$$10$ to spend? Is it an an optimal solution?

Solution:

$($c$)$ In some versions of this problem, we compute the ratio of value $($ranking$)$ to weight $($price$),$ as

shown in the table below. Using the rating$-$per$-$dollar as the way each item is evaluated, what

would a Greedy solution be assuming you have $$10$ to spend? Is it an an optimal solution?

Solution: