Question

A business orders sunglasses with a happy smiles on the arms and sells them for $50 each. During a typical month, 900 sunglasses are sold. It costs $25 to place an order and 25 percent to carry sunglasses in inventory for a year. (15 points)

a.       How many sunglasses should the bookstore order at one time (i.e., lot size, EOQ)?

b.       The supplier would like to deliver sunglasses once a week. How does this compare to the preferred lot size found in part a? Will there be additional costs to the bookstore to comply with the supplier’s request?

c.       Suppose the sales increase to 1500 sunglasses per month, but the manager decides to keep the lot size the same as in part a. How much will this decision cost the bookstore per year? Compare the TC of this decision to the TC of ordering the EOQ found in part a.

Answer 1

a. Bookstore should order 85 sunglasses at one time.

EOQ = SQRT(2*900*25/(25%*25)) = 85 Glasses.

b. If Supplier would like to deliver sunglasses once a week then he would have to place four order of 225 glasses per order which will increase its order cost to $28.125 instead of $25.

i.e. EOQ = SQRT(2*900*A/(25%*A)

SQ(225)/1800 = A/0.25A

i.e. 7.03124 * 4 = 28.125

c. If sales increase to 1500 sunglasses per month and lot size will remain same i.e. 85

Then yearly total order cost for 1500*12 = 18000 glasses would be = [(1500/85)*25] + 25% of [(1500/85)*25] = 551*12 = $6612

Total additional cost for ordering glasses in compare to part would be = TC of Parc C - Total Cost of Part a

= 6612 - 3975 = $2637