A vending machine is programmed to count out the correct change for each

transaction. Use excel to formulate and solve an IP model that will determine how change is to be made for a purchase of $$4\mathrm{.}43,$ when a $$10$ bill is inserted into the machine. This means that the machine should deliver $$5\mathrm{.}57$ to the purchaser $($i$.$e$.$ $$10-$ $$4\mathrm{.}43).$ The model$$s solution should be based on the availability of coins in the machine, with the objective of minimizing the total number of coins used to make change.

$$1$ coins available: $8$

Quarters available: $9$

Dimes available: $7$

Nickels available: $11$

Pennies available: $10$