Determine the total cost for this plan given the following forecast:

Month May Jun Jul Aug Sep Oct Nov Dec Jan Feb March April May June July

Forecast $480410420440470490480420480500480500510500520$

Use steady regular output of $400$ units per month, use overtime as needed for up to $40$ units per month, and use subcontracting to make up any needed output to match the forecast. Unit costs are:

Regular output $$35$

Overtime $$45$

Subcontract $$70$

Holding costs $$3$

Lost sales $$15$