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A Producer of photo equipment buys lenses from suppliers at $100 each. The producer requires 125 lenses per year, and the ordering cost is $18 per order. Carrying cost per unit-year (based on average inventory) is estimated to be $20 each. The supplier offers a 6 percent discount for purchases of 50 lenses and an 8 percent discount for purchases of 100 or more lenses at one time. What is the most economical amount to order at a time? Represent the solution graphically?
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A Producer of photo equipment buys lenses from suppliers at $100 each....
The Economic Order Quantity (EOQ) Model
The Economic Order Quantity (EOQ) model is a mathematical formula used to determine the optimal order quantity that minimizes the total inventory costs for a company. It takes into account the ordering cost, carrying cost, and demand for the product.
Given Information:
- Cost of lenses from suppliers: $100 each
- Annual demand: 125 lenses
- Ordering cost: $18 per order
- Carrying cost: $20 per unit-year
- Discount offered by the supplier: 6% for 50 lenses, 8% for 100 or more lenses
Economic Order Quantity (EOQ) Formula:
The EOQ formula is given by:
EOQ = sqrt((2 * D * S) / H)
Where,
D = Annual demand
S = Ordering cost per order
H = Carrying cost per unit-year
Calculating EOQ:
Using the given information, we can calculate the EOQ as follows:
EOQ = sqrt((2 * 125 * 18) / 20) = sqrt(225) = 15
Discount Analysis:
Now, let's analyze the supplier's discount offers to determine the most economical amount to order at a time.
Option 1: No Discount
If we order 15 lenses at a time without any discount, the total cost would be:
Total cost = (Ordering cost * Number of orders) + (Carrying cost per lens * EOQ)
Total cost = (18 * (125/15)) + (20 * 15) = 120 + 300 = $420
Option 2: 6% Discount for 50 lenses
If we order 50 lenses at a time to avail the 6% discount, the total cost would be:
Total cost = (Ordering cost * Number of orders) + (Carrying cost per lens * EOQ)
Total cost = (18 * (125/50)) + (20 * 50) = 45 + 1000 = $1045
Option 3: 8% Discount for 100 or more lenses
If we order 100 lenses at a time to avail the 8% discount, the total cost would be:
Total cost = (Ordering cost * Number of orders) + (Carrying cost per lens * EOQ)
Total cost = (18 * (125/100)) + (20 * 100) = 22.5 + 2000 = $2022.5
Graphical Representation:
The total cost for each ordering option can be plotted on a graph to visualize the cost difference.
Conclusion:
From the calculations and graphical representation, we can conclude that ordering 15 lenses at a time without any discount is the most economical option. It results in a total cost of $420, which is lower compared to the costs of ordering with discounts. Therefore, the producer should order 15 lenses at a time to minimize inventory costs.
The Economic Order Quantity (EOQ) model is a mathematical formula used to determine the optimal order quantity that minimizes the total inventory costs for a company. It takes into account the ordering cost, carrying cost, and demand for the product.
Given Information:
- Cost of lenses from suppliers: $100 each
- Annual demand: 125 lenses
- Ordering cost: $18 per order
- Carrying cost: $20 per unit-year
- Discount offered by the supplier: 6% for 50 lenses, 8% for 100 or more lenses
Economic Order Quantity (EOQ) Formula:
The EOQ formula is given by:
EOQ = sqrt((2 * D * S) / H)
Where,
D = Annual demand
S = Ordering cost per order
H = Carrying cost per unit-year
Calculating EOQ:
Using the given information, we can calculate the EOQ as follows:
EOQ = sqrt((2 * 125 * 18) / 20) = sqrt(225) = 15
Discount Analysis:
Now, let's analyze the supplier's discount offers to determine the most economical amount to order at a time.
Option 1: No Discount
If we order 15 lenses at a time without any discount, the total cost would be:
Total cost = (Ordering cost * Number of orders) + (Carrying cost per lens * EOQ)
Total cost = (18 * (125/15)) + (20 * 15) = 120 + 300 = $420
Option 2: 6% Discount for 50 lenses
If we order 50 lenses at a time to avail the 6% discount, the total cost would be:
Total cost = (Ordering cost * Number of orders) + (Carrying cost per lens * EOQ)
Total cost = (18 * (125/50)) + (20 * 50) = 45 + 1000 = $1045
Option 3: 8% Discount for 100 or more lenses
If we order 100 lenses at a time to avail the 8% discount, the total cost would be:
Total cost = (Ordering cost * Number of orders) + (Carrying cost per lens * EOQ)
Total cost = (18 * (125/100)) + (20 * 100) = 22.5 + 2000 = $2022.5
Graphical Representation:
The total cost for each ordering option can be plotted on a graph to visualize the cost difference.
Conclusion:
From the calculations and graphical representation, we can conclude that ordering 15 lenses at a time without any discount is the most economical option. It results in a total cost of $420, which is lower compared to the costs of ordering with discounts. Therefore, the producer should order 15 lenses at a time to minimize inventory costs.
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A Producer of photo equipment buys lenses from suppliers at $100 each. The producer requires 125 lenses per year, and the ordering cost is $18 per order. Carrying cost per unit-year (based on average inventory) is estimated to be $20 each. The supplier offers a 6 percent discount for purchases of 50 lenses and an 8 percent discount for purchases of 100 or more lenses at one time. What is the most economical amount to order at a time? Represent the solution graphically?
Question Description
A Producer of photo equipment buys lenses from suppliers at $100 each. The producer requires 125 lenses per year, and the ordering cost is $18 per order. Carrying cost per unit-year (based on average inventory) is estimated to be $20 each. The supplier offers a 6 percent discount for purchases of 50 lenses and an 8 percent discount for purchases of 100 or more lenses at one time. What is the most economical amount to order at a time? Represent the solution graphically? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A Producer of photo equipment buys lenses from suppliers at $100 each. The producer requires 125 lenses per year, and the ordering cost is $18 per order. Carrying cost per unit-year (based on average inventory) is estimated to be $20 each. The supplier offers a 6 percent discount for purchases of 50 lenses and an 8 percent discount for purchases of 100 or more lenses at one time. What is the most economical amount to order at a time? Represent the solution graphically? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Producer of photo equipment buys lenses from suppliers at $100 each. The producer requires 125 lenses per year, and the ordering cost is $18 per order. Carrying cost per unit-year (based on average inventory) is estimated to be $20 each. The supplier offers a 6 percent discount for purchases of 50 lenses and an 8 percent discount for purchases of 100 or more lenses at one time. What is the most economical amount to order at a time? Represent the solution graphically?.
A Producer of photo equipment buys lenses from suppliers at $100 each. The producer requires 125 lenses per year, and the ordering cost is $18 per order. Carrying cost per unit-year (based on average inventory) is estimated to be $20 each. The supplier offers a 6 percent discount for purchases of 50 lenses and an 8 percent discount for purchases of 100 or more lenses at one time. What is the most economical amount to order at a time? Represent the solution graphically? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A Producer of photo equipment buys lenses from suppliers at $100 each. The producer requires 125 lenses per year, and the ordering cost is $18 per order. Carrying cost per unit-year (based on average inventory) is estimated to be $20 each. The supplier offers a 6 percent discount for purchases of 50 lenses and an 8 percent discount for purchases of 100 or more lenses at one time. What is the most economical amount to order at a time? Represent the solution graphically? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Producer of photo equipment buys lenses from suppliers at $100 each. The producer requires 125 lenses per year, and the ordering cost is $18 per order. Carrying cost per unit-year (based on average inventory) is estimated to be $20 each. The supplier offers a 6 percent discount for purchases of 50 lenses and an 8 percent discount for purchases of 100 or more lenses at one time. What is the most economical amount to order at a time? Represent the solution graphically?.
Solutions for A Producer of photo equipment buys lenses from suppliers at $100 each. The producer requires 125 lenses per year, and the ordering cost is $18 per order. Carrying cost per unit-year (based on average inventory) is estimated to be $20 each. The supplier offers a 6 percent discount for purchases of 50 lenses and an 8 percent discount for purchases of 100 or more lenses at one time. What is the most economical amount to order at a time? Represent the solution graphically? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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