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answer them □1\square 1 : A bookstore sells 200 textbooks a year, it costs them ...
Sep 24, 2024
answer them
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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