KP organization procures and sells apparel items. The model number of one of the popular items is KP201. The company believes that the total minimum cost order quantity model assumptions are reasonably met for this particular model. Relevant data, from the files of the firm, are annual demand 40,000 units, unit value/price is $40, holding (or carrying) cost is 10% of the unit value/price, cost to replenish inventory $300 per order. Assume the number of working days in a year is 300.(a) What is the optimal order size?                                                                      (1 mark)(b) What is the optimal number of days between orders?                                   (1 mark)(c) What is the optimal total annual inventory cost of maintaining inventory?       (1 mark)(d) What will happen to the total inventory cost if they order all the 40,000 items in a lot in a year?                                                                                                                                       (1 mark)(e) What will be the total annual inventory cost if they replenish 1000 items per order?       (1 mark)

(a) The optimal order size can be calculated using the Economic Order Quantity (EOQ) model. The formula for EOQ is √((2DS)/H), where D is the annual demand, S is the order cost, and H is the holding cost per unit per year.

Plugging in the given values, we get:

EOQ = √((240000300)/(40*0.10)) = 2000 units

(b) The optimal number of days between orders can be calculated by dividing the number of working days in a year by the number of orders in a year. The number of orders in a year is the annual demand divided by the EOQ.

So, Days between orders = 300 / (40000 / 2000) = 15 days

(c) The optimal total annual inventory cost of maintaining inventory can be calculated using the formula: (D/EOQ)*S + (EOQ/2)*H

So, Total annual cost = (40000/2000)*300 + (2000/2)*4 = 6000 + 4000 = $10,000

(d) If they order all the 40,000 items in a lot in a year, the total inventory cost would be the cost of the order plus the holding cost for all the items. The holding cost would be half the annual demand times the holding cost per unit, as on average, half the items would be held in inventory.

So, Total cost = S + (D/2)*H = 300 + (40000/2)*4 = $80,300

(e) If they replenish 1000 items per order, the total annual inventory cost would be calculated similarly to part (c), but with the EOQ replaced by 1000.

So, Total annual cost = (40000/1000)*300 + (1000/2)*4 = 12000 + 2000 = $14,000