Wilshire Farms uses 6000 pounds per year of a special feed supplement that costs

Question

Wilshire Farms uses 6000 pounds per year of a special feed supplement that costs $5 per pound. The supplement’s supplier offers a two percent discount (to $4.90 per pound) if it is ordered in quantities of 3000 pounds or more at a time. It costs $100 to place and receive an order. Wilshire uses an inventory carrying charge of 40 percent of the supplement’s per pound value per year. Perform a cost analysis to determine whether Wilshire should use the economic order quantity (EOQ) or should order a quantity (that is not an EOQ) to take advantage of the discount. If Wilshire should use an order quantity to take advantage of the discount, what is this order quantity?

Explanation / Answer

EOQ = = [(2*annual requirement*order cost/carrying cost)]^0.5

=[(2*6,000*$100/40% of $5)]^0.5

= [(1,200,000/2)]^0.5 = 774.60 (or 775 rounded off).

Now, total cost = (order quantity/2)*carrying cost+(annual demand/order quantity)*ordering cost+price*annual demand

(774.60/2)*$2+(6000/774.6)*$100+$5*6,000

= 774.6+774.6+30,000

= $31,549.19

Now, suppose 3,00 pounds are ordered at a time.  total cost = (order quantity/2)*carrying cost+(annual demand/order quantity)*ordering cost+price*annual demand

= (3,000/2)*40% of $4.9 + (6000/3000)*100+6000*4.9

= 2940+200+29400 = $32,540.

If 6,000 pounds are ordered at a time,  total cost = (order quantity/2)*carrying cost+(annual demand/order quantity)*ordering cost+price*annual demand

= (6000/2)*40% of 4.9 + (6000/6000)*100 + 6000*4.9

= 11760+100+29400 = $41,260

Thus, the total cost is lowest when the EOQ amount of 774.60 pounds are ordered. The costs are higher, when 3,000 pounds or more are ordered to take advantage of discount.

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