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:

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.