KK manufacturing company is faced with demand for its product in each of the next four periods as shown in Table 1.  It must decide upon a production schedule to meet these demands.

Table

In any period the cost of production is $1 per unit plus a setup cost of $3.  The setup cost is not incurred if zero units are produced.  No more than six units may be produced in any period.  In addition, there is an inventory holding cost of $0.50 per unit per period.  The firm has zero inventories on hand at the beginning of period 1 and wishes to have zero inventories at the end of period 4.  The inventory capacity is five units.

Formulate this problem as dynamic programming problem and find the production schedule that meets the demand requirements at minimum cost (production plus inventory cost).