Question

3. Prefab, a furniture manufacturer, uses 20,000 square feet of plywood per month. Its trucking company charges Prefab $400 per shipment, independent of the quantity purchased. The manufacturer offers an all unit quantity discount with a price of $1 per square foot for orders under 20,000 square feet, $0.98 per square foot for orders between 20,000 square feet and 40,000 square feet, and $0.96 per square foot for orders larger than 40,000 square feet. Prefab incurs a holding cost of 20 percent.

Answer 1

Answer:

EOQ 30,984 (no discounts)

with discounts: 40,000

Explanation:

To know the best order quantity we use the Economic Order Quantity:

$Q_{opt} = \sqrt{\frac{2DS}{H}}$

Where:

D = annual demand = 20,000 per month x 12 months = 240,000 anual demand

S= setup cost = ordering cost $400

H= Holding Cost = $1 x 20% = 0.20

$Q_{opt} = \sqrt{\frac{2 \times 240,000 \times 400}{0.2}}$

EOQ = 30,983.86677

EOQ = 30,984

Now, considering there is a discount, we must check the EOQ against the next discount bracket.

below EOQ the order has less discount or equal discount, so the EOC should provide better cost.

At EOQ:

240,000 x 0.98 = 235,200

240,000/30,984 = 7.75 order per year x $400 = 3,100

30,984/2 = 15,492 average inventory x 0.2 holding cost = 3,098.4

Total Cost: 241.398,4‬

At 40,000 the cost is 0.96 per plywood:

240,000 x 0.96 = 230,400

240,000/40,000 = 12 order x $ 400 = $  4,800

40,000/2 = 20,000 average inventory x 0.2 holding cost: $  4,000

Total Cost: 239,200

after taking the discount into account the best deal is to take orders for 40,000 units

Increasing this will increase the holding cost, thus increasing the inventory cost.