Problem 13-4 A large law firm uses an average of 42 boxes of copier paper a day.
ID: 444215 • Letter: P
Question
Problem 13-4 A large law firm uses an average of 42 boxes of copier paper a day. The firm operates 257 days a year. Storage and handling costs for the paper are $26 a year per box, and it costs approximately $58 to order and receive a shipment of paper.
a. What order size would minimize the sum of annual ordering and carrying costs? (Round your answer to the nearest whole number.) Order size boxes
b. Compute the total annual cost using your order size from part a. (Round intermediate calculations and final answer to 2 decimal places. Omit the "$" sign in your response.) Total annual cost $
c. Except for rounding, are annual ordering and carrying costs always equal at the EOQ? Yes No d-1. The office manager is currently using an order size of 196 boxes. The partners of the firm expect the office to be managed "in a cost-efficient manner." compute total cost for this current order size. (Round intermediate calculations and final answer to 2 decimal places. Omit the "$" sign in your response.) TC = $
d-2. Would you recommend that the office manager use the optimal order size instead of 196 boxes? Yes? No?
rev: 02_25_2012
Explanation / Answer
Annual demand D = 257*42 units = 10794 units
Holding cost H = $26/unit
Ordering cost S = $58/order
The economic order quantity minimizes the sum of ordering and holding cost.
a. Thus, Economic order quanitity Q = sqrt(2*D*S/H) = 219.45 ~ 220 units
b. Now, total cost = Ordering cost+Holding cost
For ordering cost, number of orders = 257*42/220 = 49.06 ~ 50 orders
Thus, ordering cost = Number of orders * Ordering cost/order = 50*58 = $2900
Holding cost = (1/2)*H*Q = (1/2)*26*220 = $2860
Thus, total cost = 2900+2860 = $5760
c. Yes, annual ordering and holding costs are always equal at EOQ
d-1. For ordering size of 196 boxes, total cost = ordering cost + holding cost
For Ordering cost, number of orders = 257*42/196 = 55.07 ~ 56 orders (As number of orders has to be a whole number)
Thus, ordering cost= $56*58 = $3248
Holdinig cost = (1/2)*H*Q = (1/2)*26*196 = $2548
Thus, total cost = $(3248+2548) = $5796
d-2. Yes, office maanger should use optimum size as total cost for optimum size is lesser than that for 196 units
Total cost for optimum size = $5760 while that for 196 units = $5796