Bits and Pieces uses overtime, inventory, and subcontracting to absorb fluctuations in demand. An annual production plan is devised and updated quarterly. Expected demand over the next four quarters is $600,800,1600,$ and $1900$ units, respectively. The capacity for regular production is $1000$ units per quarter with an overtime capacity of $100$units a quarter. Subcontracting is limited to $500$ units a quarter. Regular production costs $$20$ per unit, overtime $$30$ per unit, and subcontracting $$28$ per unit. Inventory holding costs are assessed at $$5$per unit per period. There is no beginning inventory. Design a production plan that will satisfy demand at minimum cost.