$1.$Suppose that a country decided to use $25$ cent, $15$ cent, $2$ cent, and $1$ cent coins. Use the Greedy Algorithm to make change for $30$ cents. Does this algorithm give you an optimal solution, one that uses the fewest number of coins? Explain.

$2.$ Suppose that a country decided to use $25$ cent, $15$ cent, $4$ cent, and $2$ cent coins. Use the Greedy Algorithm to make change for $30$ cents. Does this algorithm give you an optimal solution, one that uses the fewest number of coins? Explain.