Brown's, distributor of three models of Lawn Mowers, $($A$,$ B$,$ C$)$ has decided to aggregate and order all three models each time they place an order $($joint order and delivery$).$ The annual demand for the three products is $12000,1200,$ and $120$ units respectively. Each model costs the wholesaler five hundred dollars $($$$500).$ A fixed transportation cost of $$4000$ is incurred each time an order is delivered. For each model ordered and delivered, an additional fixed cost of $$1000$ is incurred for receiving and storage. Mr Brown incurs a holding cost of $20$ per cent.

Determine the following:

$1$ combined order cost per order $(3$ marks$)$

$11$ optimal order frequency $(3$ marks$)$

Ili annual order cost $(1$ mark$)$

annual holding cost $(3$ marks$)$

total annual cost across all three models $(3$ marks$)$ please show all workings