Problem 2: You are working at the cash register at the local supermarket and you have to make change for n cents. To save time (and be nice to your customers) you want to do that with the fewest number of coins Dacribe a greedy algorithm to make change when the coins in the drawer are the usual US, coin denominations: quarters, dimes, nickels and pennies. Argue that the gredy algorithm yields an optimal solution. What if you were working in the country of Powerpolis where coins denominations are ee for some integer c>1 and k 2 1. Does the greedy algorithm still yields an optimal solution? Show an example of a set of coin denominations for which the greedy algorithm does not yield an optimal solution