Mrs. Lopez is working as as a cashier at the local convenience store. A customer's bill is $1.09, and the customer gave Mrs. Lopez $2.00. She wants to give him change using the smallest possible number of coins. Use dynamic programming to determine how to give the customer his change.

Resolve the problem if a 20c piece were available. *US coins: 10, 5c, 100, 250, 50 and $1.

Solution must include definition of stage/s, alternative/s, states, recursive equations, complete rows and columns per table, optimal solution, and corresponding conclusions.