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answer them □1\square 1 : A bookstore sells 200 textbooks a year, it costs them ...
Sep 24, 2024
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Solution by Steps
Problem 1:
step 1
The EOQ formula is given by EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D D is the demand, S S is the ordering cost, and H H is the holding cost. For the bookstore, D=200 D = 200 , S=20 S = 20 , and H=5 H = 5
step 2
Substituting the values into the formula: EOQ=2×200×205 \mathrm{EOQ} = \sqrt{\frac{2 \times 200 \times 20}{5}}
step 3
Calculating: EOQ=80005=1600=40 \mathrm{EOQ} = \sqrt{\frac{8000}{5}} = \sqrt{1600} = 40
step 4
Therefore, the EOQ for the bookstore is 40 40
Problem 2:
step 1
For the hardware store, using the same EOQ formula EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D=450 D = 450 , S=15 S = 15 , and H=2 H = 2
step 2
Substituting the values: EOQ=2×450×152 \mathrm{EOQ} = \sqrt{\frac{2 \times 450 \times 15}{2}}
step 3
Calculating: EOQ=6750=1530≈82.16 \mathrm{EOQ} = \sqrt{6750} = 15\sqrt{30} \approx 82.16
step 4
Therefore, the EOQ for the hardware store is approximately 82.16 82.16
Problem 3:
step 1
For the shop, using the EOQ formula EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D=800 D = 800 , S=10 S = 10 , and H=3 H = 3
step 2
Substituting the values: EOQ=2×800×103 \mathrm{EOQ} = \sqrt{\frac{2 \times 800 \times 10}{3}}
step 3
Calculating: EOQ=160003=40303≈73.03 \mathrm{EOQ} = \sqrt{\frac{16000}{3}} = \frac{40\sqrt{30}}{3} \approx 73.03
step 4
Therefore, the EOQ for the shop is approximately 73.03 73.03
Problem 4:
step 1
For the company, using the EOQ formula EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D=5000 D = 5000 , S=50 S = 50 , and H=10 H = 10
step 2
Substituting the values: EOQ=2×5000×5010 \mathrm{EOQ} = \sqrt{\frac{2 \times 5000 \times 50}{10}}
step 3
Calculating: EOQ=50000=1005≈223.61 \mathrm{EOQ} = \sqrt{50000} = 100\sqrt{5} \approx 223.61
step 4
Therefore, the EOQ for the company is approximately 223.61 223.61
Problem 5:
step 1
For the grocery store, using the EOQ formula EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D=1200 D = 1200 , S=30 S = 30 , and H=4 H = 4
step 2
Substituting the values: EOQ=2×1200×304 \mathrm{EOQ} = \sqrt{\frac{2 \times 1200 \times 30}{4}}
step 3
Calculating: EOQ=18000=605≈134.16 \mathrm{EOQ} = \sqrt{18000} = 60\sqrt{5} \approx 134.16
step 4
Therefore, the EOQ for the grocery store is approximately 134.16 134.16
Answer
Problem 1: 40
Problem 2: 82.16
Problem 3: 73.03
Problem 4: 223.61
Problem 5: 134.16
Key Concept
The Economic Order Quantity (EOQ) is a formula used to determine the optimal order quantity that minimizes total inventory costs.
Explanation
The EOQ helps businesses manage their inventory efficiently by balancing ordering costs and holding costs, leading to cost savings and improved inventory management.
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Solution by Steps
step 1
The EOQ formula is given by EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D D is the demand, S S is the ordering cost, and H H is the holding cost. For the bookstore, D=200 D = 200 , S=20 S = 20 , and H=5 H = 5
step 2
Substituting the values into the formula: EOQ=2×200×205 \mathrm{EOQ} = \sqrt{\frac{2 \times 200 \times 20}{5}}
step 3
Calculating the numerator: 2×200×20=8000 2 \times 200 \times 20 = 8000 and then dividing by H H : 80005=1600 \frac{8000}{5} = 1600
step 4
Taking the square root gives EOQ=1600=40 \mathrm{EOQ} = \sqrt{1600} = 40
Answer
40
Key Concept
Economic Order Quantity (EOQ) is a formula used to determine the optimal order quantity that minimizes total inventory costs.
Explanation
The EOQ for the bookstore is calculated to be 40, which means ordering 40 textbooks at a time will minimize the total costs associated with ordering and holding inventory.
---
step 1
The EOQ formula is given by EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D=450 D = 450 , S=15 S = 15 , and H=2 H = 2 for the hardware store
step 2
Substituting the values into the formula: EOQ=2×450×152 \mathrm{EOQ} = \sqrt{\frac{2 \times 450 \times 15}{2}}
step 3
Calculating the numerator: 2×450×15=13500 2 \times 450 \times 15 = 13500 and then dividing by H H : 135002=6750 \frac{13500}{2} = 6750
step 4
Taking the square root gives EOQ=6750≈82.5 \mathrm{EOQ} = \sqrt{6750} \approx 82.5
Answer
Approximately 82.5
Key Concept
Economic Order Quantity (EOQ) helps businesses determine the most cost-effective quantity to order.
Explanation
The EOQ for the hardware store is approximately 82.5, indicating that ordering around 83 hammers at a time will minimize costs.
---
step 1
The EOQ formula is given by EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D=800 D = 800 , S=10 S = 10 , and H=3 H = 3 for the shop
step 2
Substituting the values into the formula: EOQ=2×800×103 \mathrm{EOQ} = \sqrt{\frac{2 \times 800 \times 10}{3}}
step 3
Calculating the numerator: 2×800×10=16000 2 \times 800 \times 10 = 16000 and then dividing by H H : 160003≈5333.33 \frac{16000}{3} \approx 5333.33
step 4
Taking the square root gives EOQ≈73 \mathrm{EOQ} \approx 73
Answer
Approximately 73
Key Concept
EOQ is a critical inventory management tool that helps in minimizing costs.
Explanation
The EOQ for the shop is approximately 73, suggesting that ordering this quantity will help in reducing overall inventory costs.
---
step 1
The EOQ formula is given by EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D=5000 D = 5000 , S=50 S = 50 , and H=10 H = 10 for the company
step 2
Substituting the values into the formula: EOQ=2×5000×5010 \mathrm{EOQ} = \sqrt{\frac{2 \times 5000 \times 50}{10}}
step 3
Calculating the numerator: 2×5000×50=500000 2 \times 5000 \times 50 = 500000 and then dividing by H H : 50000010=50000 \frac{500000}{10} = 50000
step 4
Taking the square root gives EOQ=50000≈223.61 \mathrm{EOQ} = \sqrt{50000} \approx 223.61
Answer
Approximately 223.61
Key Concept
EOQ is essential for optimizing inventory levels and reducing costs.
Explanation
The EOQ for the company is approximately 224, indicating the optimal order quantity to minimize costs.
---
step 1
The EOQ formula is given by EOQ=2DSH \mathrm{EOQ} = \sqrt{\frac{2DS}{H}} where D=1200 D = 1200 , S=30 S = 30 , and H=4 H = 4 for the grocery store
step 2
Substituting the values into the formula: EOQ=2×1200×304 \mathrm{EOQ} = \sqrt{\frac{2 \times 1200 \times 30}{4}}
step 3
Calculating the numerator: 2×1200×30=72000 2 \times 1200 \times 30 = 72000 and then dividing by H H : 720004=18000 \frac{72000}{4} = 18000
step 4
Taking the square root gives EOQ=18000≈134.16 \mathrm{EOQ} = \sqrt{18000} \approx 134.16
Answer
Approximately 134.16
Key Concept
EOQ is a vital metric for managing inventory effectively.
Explanation
The EOQ for the grocery store is approximately 134, which helps in minimizing the total costs associated with ordering and holding inventory.
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