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Sagot :
Answer: a. $124.59
b. 57%
Explanation:
Monthly demand = 610
Annual demand (D) = 610 x 12 = 7,320
Cost (C) = $2.70 each
Annual carrying costs (Cc) = 50% of cost = 50% × $2.70 = $1.35
Ordering costs (Co) = $30
Current order quantity (Q1) = 1,000
a. What additional annual cost is the shop incurring by staying with this order size?
Current cost will be:
= [(1000 / 2) x $1.35] + [(7320 / 1000) x $30]
= (500 × $1.35) + (7.32 × $30)
= $675 + $219.60
= $894.60
Then, the optimal order quantity will be calculated as:
Q = ✓[(2 x D x Co) / Cc]
Q = ✓[(2 x 7320 x 30) / 1.35]
Q = 570.38
Q = 570
Therefore, the optimal order quantity is 570 units.
New cost will be:
= [(570 / 2) x $1.35] + [(7320 / 570) x $30]
= $384.75 + $385.26
New cost = $770.01
Additional annual cost will then be:
= $894.6 - $770.01
= $124.59
b. Other than cost savings, what benefit would using the optimal order quantity yield (relative to the order size of 1,000
Storage space will be:
= (570 / 1000) x 100
= 57%
Therefore, about 57% of the storage space would be needed.
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