A small manufacturing firm uses roughly 3400 pounds of chemical dye a year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The supplier has just announced that order of 1000 pounds or more will be filled at a price of $2 per pound. The manufacturing firm incurs a cost of $100 for each time it submits an order and assigns an annual holding cost of 17 percent of the purchase price per pound. Determine the order size that will minimize the total cost. (enter answer in pounds with no decimal)

Consider the following calculations

Explanation:

First calculate the Economic Order Quantity (EOQ) ignoring the discount.

Economic Order Quantity (EOQ) = √ (2DS/H)

D - Demand per year = 3400 pounds

S - Ordering cost per year = $100

Per unit cost = $3 per pound

H - Holding (carrying) cost per unit per year=$0.51 (17% of purchase price)

So by applying the above formula, we get the following answer:

EOQ = SQRT (2*3400*100/0.51) = 1154.70 units

Economic Order Quantity (EOQ) = 1154 units

Discounted Order Quantity (DOQ) = 1500 units

Annual Orders under EOQ = Demand : EOQ = 3400 : 1154 = 3 orders

Annual Orders under DOQ = Demand : DOQ = 3400: 1500 = 2.40 or 3 orders

Average Inventory under EOQ = EOQ : 3 = 1154 : 3 = 384.90 units

Average Inventory under DOQ = DOQ : 3 = 1500 : 3 = 500 units

A-Saving from reduction in Price

= Demand * Full Price * Discount Rate

= 3400 * 3 * 0.33 = $ 3366

B-Saving from reduction in orders

= Orders reduced * Order Cost

= (3 - 3) * 100 = 0

C-Increase in holding cost

= Increase in average inventory * holding cost per unit per annum

Holding cost is 17% of purchase price

So for 500 units it is=$170 (17% of $2 per pound)

For 384.90 units = $196.30 (17% of $3 per pound)

Increase in holding cost = 170-196.30 = $-26.30

Net savings on discount order quantity = A + B - C = 3366 + 0 - (-26.30) = $3392.30

Since the net effect on income is positive, the store should place the order for quantity discount.