Computronics is a manufacturer of calculators, currently producing 200 per week. One component for every calculator is a liquid crystal display (LCD), which the company purchases from Displays, Inc. (DI) for $1 per LCD. Computronics management wants to avoid any shortage of LCDs, since this would disrupt production, so DI guarantees a delivery time of  week on each order. The placement of each order is estimated to require 1 hour of clerical time, with a direct cost of $15 per hour plus overhead costs of another $5 per hour. A rough estimate has been made that the annual cost of capital tied up in Computronics' inventory is 15 percent of the value (measured by purchase cost) of the inventory. Other costs associated with storing and protecting the LCDs in inventory amount to 5 cents per LCD per year.

(a) What should the order quantity and reorder point be for the LCDs? What is the corresponding total variable inventory cost per year (holding costs plus administrative costs for placing orders)?

(b) Suppose the true annual cost of capital tied up in Computronics' inventory actually is 10 percent of the value of the inventory. Then what should the order quantity be? What is the difference between this order quantity and the one obtained in part (a)? What would the total variable inventory cost per year (TVC) be? How much more would TVC be if the order quantity obtained in part (a) still were used here because of the incorrect estimate of the cost of capital tied up in inventory?

(c) Repeat part (b) if the true annual cost of capital tied up in Computronics' inventory actually is 20 percent of the value of the inventory.

(d) Perform sensitivity analysis systematically on the unit holding cost by generating a table that shows what the optimal order quantity would be if the true annual cost of capital tied up in Computronics' inventory were each of the following percentages of the value of the inventory: 10, 12, 14, 16, 18, 20.

(e) Assuming that the rough estimate of 15 percent is correct for the cost of capital, perform sensitivity analysis on the setup cost by generating a table that shows what the optimal order quantity would be if the true number of hours of clerical time required to place each order were each of the following: 0.5, 0.75, 1, 1.25, 1.5.

(f) Perform sensitivity analysis simultaneously on the unit holding cost and the setup cost by generating a table that shows the optimal order quantity for the various combinations of values considered in parts (d) and (e).