Question: A vending machine is programmed to count out the correct change for each transaction. Formulate an integer linear program model that will determine how change is to be made for a purchase of $7.33, when a $10 bill is inserted into the machine. The solution to the model should be based on the availability of the coins in the machine, with the objective of minimizing the total number of coins used to make the change. The table below shows the denomination of coins in the machine and their availability. (Hint: make sure the linear program knows the exact amount of money that needs to be returned).
| Denomination |
Availability |
| $1 coin |
2 |
| Quarter($0.25) |
7 |
| Dime($0.10) |
6 |
| Nickel($0.05) |
5 |
| Peny($0.01) |
4 |
a) How many decision variables does this problem have?
b) Not counting the non-negativity constraint - how many constraints does this problem have?
c) How many coins are returned to the customer when the machine makes the change?