Answer:
EOQ 30,984 (no discounts)
with discounts: 40,000
Explanation:
To know the best order quantity we use the Economic Order Quantity:
[tex]Q_{opt} = \sqrt{\frac{2DS}{H}}[/tex]
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
[tex]Q_{opt} = \sqrt{\frac{2 \times 240,000 \times 400}{0.2}}[/tex]
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.
