The manager at a local university bookstore wishes to apply the EOQ model to determine the respective order quantities for two products: ballpoint pens and mechanical pencils. The annual demand for pens and pencils is 1500 and 400, respectively. The ordering cost for each product is $20 per order and the wholesale price of a pen and pencil is $1.50 and $4, respectively. Assume the bookstore's annual holding rate is 10% and that the bookstore operates 240 days per year.

a. Determine the optimal order quantity and the order cycle time for each product. What is the total cost (summed over both products)?

b. The bookstore orders the pens and pencils from the same supplier. If these two products had the same cycle time, the corresponding shipment consolidation would reduce the ordering cost to $15. How much money does the bookstore save by consolidating the orders for these two products? (By setting the cycle times equal, we have Qpens/(1500/240) = Qpencils/(400/240) or Qpens = 3.75Qpencils). Make this substitution into the combined cost equation so that it is a function only of Qpencils and apply equation (10.5) with the appropriate values to determine Qpencils (and subsequently Qpens).