A manager is attempting to put together an aggregate plan for the coming nine months. She has obtained a forecast of expected demand for the planning horizon. The plan must deal with highly seasonal demand; demand is relatively high in periods $3$ and $4$ and again in period $8,$ as can be seen from the following forecasts:

$\backslash$table$[[$Period$,1,2,3,4,5,6,7,8,9,$Total$],[$Forecast$,190,230,260,280,210,170,160,260,180,1,940]]$

The department now has $20$ full$-$time employees, each of whom can produce $10$ units of output per period at a cost of $$6$ per unit. Inventory carrying cost is $$5$ per unit per period, and backlog cost is $$10$ per unit per period. The manager is considering a plan that would involve hiring two extra employees to start working in period $1,$ with one of them being on a temporary basis and would work only through period $5.$ Determine the total cost of the plan, including production, inventory, and back$-$order costs.