$2.(20$ pts$)$ Dessouky Enterprises has collected the following information relating to one of its major products:

Regular production available: $1400$ units per period

Regular production cost: $\backslash (\backslash$$ $10\backslash )$ per unit

Undertime production cost: $\backslash (\backslash$$ $5\backslash )$ per unit

Overtime production cost: $\backslash (\backslash$$ $15\backslash )$ per unit

Inventory costs: $\backslash (\backslash$$ $3\backslash )$ per unit per period $($use average inventory to compute costs$)$

Backorder costs: $\backslash (\backslash$$ $7\backslash )$ per unit per period

Beginning inventory: $200$ units

Quarterly demand: $2000,1500,1300,1800$

Compute the total costs associated with a level production plan. The level amount must be computed from the demand and beginning inventory.