Question

A firm has been ordering on the basis of EOQ for a product that has an annual requirement of 22,000 units/year and the unit cost is $40/unit. Ordering and receiving costs are $75/order, and the annual carrying costs are 30% of the part value in storage. The supplier is offering a 5% price discount on orders greater than 800 units/order.

Determine the EOQ without considering the quanitity discount

What is the total annual cost including the value of the product without a discount?

What is the total annual cost including the value of the product if the order quantity goes to 800 and the discount is taken?

Should the customer order the discount quantity?

Show all work.

Answer 1

Solution:-

(A). Economic order quantity =

carrying cost = 30% of unit cost

carrying cost = 0.30 x $ 40

carrying cost = $ 12

EOQ = 524 units

(B) Total annual cost = ordering cost + holding cost

Total annual cost = (D/Q) * s +( Q/2) * h

Total annual cost = ( 22,000/524) x $ 75 + ( 524/2) x $ 12

Total annual cost = $ 6,293

Value of the product without discount = $ 40

(C). If the discount is taken

value of the product = $ 40 - 0.05 x $ 40

value of the product with discount = $ 38

carring cost = 30% of $ 38

carrying cost = $ 11.40        

EOQ = 800 units

Total annual cost = ( 22,000/800) x $ 75 + ( 800/2) x $ 11.40

Total annual cost = $ 6,622.50

(D). The customer should not order the discount quantity because the total annual cost by taking the discount is greater than the total annual cost by not taking the discount .