The office manager for the Metro Life Insurance Company orders letterhead stationery from an office products firm in boxes of 500 sheets. The company uses 6500 boxes per year. Annual carrying costs are $3 per box, and ordering costs are $28. The following discount price schedule is provided by the office supply company: ORDER QUANTITY (BOXES) PRICE PER BOX 200–999 $16 1000–2999 14 3000–5999 13 6000+ 12 Determine the optimal order quantity and the total annual inventory cost.

The EOQ formula cannot be used here because the price of the goods varies according to the size of the purchase order. In this case, the order quantity that decreases annual inventory costs is 3,000 units per order, and total annual inventory costs = $89,060.67.

Step-by-step explanation:

if we apply the EOQ formula:

Economic order quantity (EOQ) = √[(2 x S x D)/H]
S = ordering cost = $28
D = annual demand = 6,500
H = holding cost = $3
EOQ = √[(2 x $28 x 6,500)/$3] = 348.33 ≈ 348 boxes

total annual inventory cost = [(6,500 / 348) x $28] + [(348 / 2) x $3] + (6,500 x $16) = $522.99 + $522 + $104,000

but if the company tried to benefit from discounts due to higher order quantities, total annual cost would be lower:

[(6,500 / 1,000) x $28] + [(1,000 / 2) x $3] + (6,500 x $14) = $182 + $1,500 + $91,000 = $92,682

[(6,500 / 3,000) x $28] + [(3,000 / 2) x $3] + (6,500 x $13) = $60.67 + $4,500 + $84,500 = $89,060.67