$1.(30$ points$)$ Greedy Algorithms. You$$re the production manager of the Acme Balloon

Company. Your company fills the character balloons for the Macy$$s Thanksgiving Day

Parade. Each year, there are n character balloons to be filled, each numbered from $1$ to

n$.$ There$$s also an associated volume for each balloon Vi$.$ And your profits are based on

the total volume of the filled balloons. However, your production facility can only fill

one balloon a day, and each balloon loses a fixed percentage $($P $)$ of its volume per day.

a$.$ Write a greedy, pseudo$-$code algorithm to determine which order the balloons should

be filled to maximize the total volume of the balloons.

b$.$ Use your algorithm with fixed percentage of volume loss P $=0\mathrm{.}02$ and this assort$-$

ment of balloons:

Balloon $12345$

Character Scooby$-$Do Garfield Goku Olaf Po

Volume $110210310330150$

$2$