A raw material, which will used during production, is purchased from an outside supplier. The company wants to make a purchasing plan for the next 4 months to determine how much and when to order to obtain the optimal minimum total cost which includes purchasing, ordering and inventory holding cost. The monthly demands for the raw material are 510, 512, 520, 565 units respectively in the next 4 months where 510 512 520 565. It costs $2, $4, $3 to keep one unit of this raw material in their warehouse for one month, during month 1, 2 and 3, respectively. Additionally, 2 4 3. Note that inventory holding cost is charged based on ending inventory (So no need for another cost since the demand of month 4 will be met in month 4 and no ending inventory will be left at the end of month 4). Unit ordering cost is fixed and represented by $116 for all months. Let $8, $6, $5, $10 represent the unit purchasing cost for the raw material for months 1, 2, 3, 4, respectively. Moreover, 8 6 5 10.

a) Find the optimal lot sizing policy (when and how much to order). If there is more than one optimal policy, write them separately.

b) Compute the optimal total cost by breaking it down into 3 components and computing the cost for each individually:

i) purchasing cost,

ii) ordering cost,

iii) inventory holding cost.