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answer these questions □\square One of the top-selling items in the container g...
Sep 24, 2024
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Solution by Steps
For Question 1: What is the annual cost of the current policy of using a 390-unit lot size?
step 1
Calculate the annual demand: The weekly demand is 18 units, so the annual demand is given by 18×52 18 \times 52
step 2
The annual demand is 18×52=936 18 \times 52 = 936 units
step 3
Calculate the number of orders per year: The number of orders is given by Annual DemandLot Size=936390 \frac{\text{Annual Demand}}{\text{Lot Size}} = \frac{936}{390}
step 4
The number of orders per year is 936390≈2.4 \frac{936}{390} \approx 2.4 orders
step 5
Calculate the ordering cost: The ordering cost is given by Number of Orders×Cost per Order=2.4×45 \text{Number of Orders} \times \text{Cost per Order} = 2.4 \times 45
step 6
The ordering cost is 2.4×45=108 2.4 \times 45 = 108 dollars
step 7
Calculate the holding cost: The holding cost is given by Lot Size2×Holding Cost per Unit=3902×(0.25×560) \frac{\text{Lot Size}}{2} \times \text{Holding Cost per Unit} = \frac{390}{2} \times (0.25 \times 560)
step 8
The holding cost is 195×140=27300 195 \times 140 = 27300 dollars
step 9
Calculate the total annual cost: The total annual cost is the sum of the ordering cost and holding cost, 108+27300=27408 108 + 27300 = 27408
Answer
The annual cost of the current policy using a 390-unit lot size is $27,408.
--- For Question 2: Would a lot size of 468 be better?
step 1
Calculate the number of orders per year for a lot size of 468: 936468 \frac{936}{468}
step 2
The number of orders per year is 936468=2 \frac{936}{468} = 2 orders
step 3
Calculate the ordering cost for a lot size of 468: 2×45 2 \times 45
step 4
The ordering cost is 2×45=90 2 \times 45 = 90 dollars
step 5
Calculate the holding cost for a lot size of 468: 4682×(0.25×560) \frac{468}{2} \times (0.25 \times 560)
step 6
The holding cost is 234×140=32760 234 \times 140 = 32760 dollars
step 7
Calculate the total annual cost for a lot size of 468: 90+32760=32850 90 + 32760 = 32850
Answer
The total annual cost for a lot size of 468 is $32,850, which is higher than the cost for 390 units. Thus, 390 units is better.
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Key Concept
The Economic Order Quantity (EOQ) model helps determine the optimal order size that minimizes total inventory costs.
Explanation
The analysis shows that using a lot size of 390 units results in lower total annual costs compared to a lot size of 468 units, making it the more cost-effective choice for the museum gift shop.
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