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Answer:
The optimal total annual inventory cost is:
= $1,512,588
by ordering 51 units with each order.
Explanation:
a) Data and Calculations:
Annual demand of computers = 3,000
Annual inventory carrying cost = 20% of unit cost
Ordering costs per order = $10
Options
Quantity Price per Unit ($)
1-25 $475.00
26-50 $445.00
51+ $420.00
Total annual inventory cost:
With 1 = 25 units at $475,
EOQ = square root of (2 * D * Ordering cost)/Holding cost
=(2 * 3,000 * $10)/$95
= 25 units
Total inventory costs when each order is 25 units:
Unit costs = $1,425,000 (3,000 * $475)
Ordering cost = $1,200 ($10 * 3,000/25)
Holding cost = $285,000 ($1,425,000 * 20%)
Total annual inventory costs = $1,711,200
With 26 - 50 units at $445,
EOQ = square root of (2 * D * Ordering cost)/Holding cost
= (2 * 3,000 * 10)/$89
= 26 units
Total inventory costs when each order is 26 units:
Unit costs = $1,335,000 (3,000 * $445)
Ordering cost = $1,154 ($10 * 3,000/26)
Holding cost = $267,000 ($1,335,000 * 20%)
Total annual inventory costs = $1,603,154
With 51+ units at $420,
EOQ = square root of (2 * D * Ordering cost)/Holding cost
= (2 * 3,000 * 10)/$84
= 27 units
Total inventory costs when each order is 27 units:
Unit costs = $1,335,000 (3,000 * $445)
Ordering cost = $1,111 ($10 * 3,000/27)
Holding cost = $267,000 ($1,335,000 * 20%)
Total annual inventory costs = $1,603,111
Total inventory costs when each order is 51 units:
Unit costs = $1,260,000 (3,000 * $420)
Ordering cost = $588 ($10 * 3,000/51)
Holding cost = $252,000 ($1,260,000 * 20%)
Total annual inventory costs = $1,512,588
However, to take advantage of the reduced cost per unit due to discount, ordering 51 units per order minimizes the total inventory cost.