1. Ordering 204 boxes will minimize the sum of annual ordering and carrying costs
2. Total cost will be $6118.82
3. Yes,annual ordering and carrying costs always equal at the EOQ.
Explanation:
D = 40 boxes per for 260 days
= [tex]40 \times 260 = 10400[/tex] boxes
S = $60
H = $30
1. [tex]Q = \sqrt{\frac{2DS}{H} }[/tex]
[tex]= \sqrt{\frac{2 \times 10400 \times 60}{30} }[/tex]
= 203.96
Q = 204 boxes
2. [tex]TC = \frac{Q \times H}{2} + \frac{D \times S}{Q}[/tex]
[tex]= \frac{204 \times 30}{2} + \frac{10400 \times 60}{204}[/tex]
[tex]= 3060 + 3058.82[/tex]
TC= $6118.82
The order size that would minimize the sum of annual ordering and carrying costs will be 204 boxes.
It should be noted that the order size is calculated as:
= (2 × 10400 × 6) / 30
= 124800/30
= 4160
= ✓4160
= 204 boxes.
The total annual cost will be calculated thus:
= 204/2(30) + 10400/204(60)
= 3060 + 3058.82
= 6118.82
It should be noted that ordering and carrying costs always equal at the EOQ.
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