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

$\backslash$table$[[$DENOMINATION$,$AVALLABILITY$],[$SI coin,$8],[$Quarter $($$$0\mathrm{.}25),9],[$Dime $($$$0\mathrm{.}10),7],[$Nickel $($$$0\mathrm{.}05),11],[$Penny $($$$0\mathrm{.}01),10]]$