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The daily demand for a commodity is given as 200 units. A fixed cost of Rs.1000 is incurred every time an order is placed. The carrying cost is given as Rs. 0.02 per unit per day. The minimum annual inventory cost is _____________
- a)32640
- b)32650
Correct answer is between ' 32640, 32650'. Can you explain this answer?
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Verified Answer
The daily demand for a commodity is given as 200 units. A fixed cost ...
Given data,
Demand = 200 units/day
= 200 × 365 units/year
= 73,000 units/year
Ordering cost = Rs. 1000/order
CC = Rs. 0.02/unit/day
= 0.02 × 365/unit/year
TC = Rs. 32646.59 /year
Most Upvoted Answer
The daily demand for a commodity is given as 200 units. A fixed cost ...
Given data,
Demand = 200 units/day
= 200 × 365 units/year
= 73,000 units/year
Ordering cost = Rs. 1000/order
CC = Rs. 0.02/unit/day
= 0.02 × 365/unit/year
TC = Rs. 32646.59 /year
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Community Answer
The daily demand for a commodity is given as 200 units. A fixed cost ...
To calculate the minimum annual inventory cost, we need to consider both the ordering cost and the carrying cost. Let's break down the calculation into the following steps:
Step 1: Calculate the number of orders placed per year
The daily demand for the commodity is given as 200 units. To calculate the number of orders placed per year, we divide the total demand by the order quantity. Let's assume the order quantity is denoted by Q.
Total demand per year = 200 units/day * 365 days/year = 73,000 units/year
Number of orders placed per year = Total demand per year / Order quantity (Q)
Step 2: Calculate the optimum order quantity (Q)
The optimum order quantity can be calculated using the Economic Order Quantity (EOQ) formula. The EOQ formula is given as:
Q = sqrt((2 * D * S) / H)
Where:
D = Annual demand (73,000 units/year)
S = Ordering cost per order (Rs. 1000)
H = Carrying cost per unit per year (Rs. 0.02)
Substituting the given values into the formula, we can calculate the optimum order quantity (Q).
Step 3: Calculate the annual ordering cost
The annual ordering cost is the product of the number of orders placed per year and the ordering cost per order.
Annual ordering cost = Number of orders placed per year * Ordering cost per order
Step 4: Calculate the annual carrying cost
The annual carrying cost is the product of the average inventory level and the carrying cost per unit per year.
Average inventory level = Q / 2
Annual carrying cost = Average inventory level * Carrying cost per unit per year
Step 5: Calculate the minimum annual inventory cost
The minimum annual inventory cost is the sum of the annual ordering cost and the annual carrying cost.
Minimum annual inventory cost = Annual ordering cost + Annual carrying cost
Now, let's calculate the values and find the minimum annual inventory cost.
Q = sqrt((2 * 73,000 * 1000) / 0.02) ≈ 32647.62 units (approx.)
Number of orders placed per year = 73,000 / 32647.62 ≈ 2.238 orders (approx.)
Annual ordering cost = 2.238 * 1000 = Rs. 2238
Average inventory level = 32647.62 / 2 ≈ 16323.81 units (approx.)
Annual carrying cost = 16323.81 * 0.02 = Rs. 326.4762 ≈ Rs. 326.48 (approx.)
Minimum annual inventory cost = 2238 + 326.48 ≈ Rs. 2564.48 (approx.)
Therefore, the minimum annual inventory cost is between Rs. 32640 and Rs. 32650 (approx.).
Step 1: Calculate the number of orders placed per year
The daily demand for the commodity is given as 200 units. To calculate the number of orders placed per year, we divide the total demand by the order quantity. Let's assume the order quantity is denoted by Q.
Total demand per year = 200 units/day * 365 days/year = 73,000 units/year
Number of orders placed per year = Total demand per year / Order quantity (Q)
Step 2: Calculate the optimum order quantity (Q)
The optimum order quantity can be calculated using the Economic Order Quantity (EOQ) formula. The EOQ formula is given as:
Q = sqrt((2 * D * S) / H)
Where:
D = Annual demand (73,000 units/year)
S = Ordering cost per order (Rs. 1000)
H = Carrying cost per unit per year (Rs. 0.02)
Substituting the given values into the formula, we can calculate the optimum order quantity (Q).
Step 3: Calculate the annual ordering cost
The annual ordering cost is the product of the number of orders placed per year and the ordering cost per order.
Annual ordering cost = Number of orders placed per year * Ordering cost per order
Step 4: Calculate the annual carrying cost
The annual carrying cost is the product of the average inventory level and the carrying cost per unit per year.
Average inventory level = Q / 2
Annual carrying cost = Average inventory level * Carrying cost per unit per year
Step 5: Calculate the minimum annual inventory cost
The minimum annual inventory cost is the sum of the annual ordering cost and the annual carrying cost.
Minimum annual inventory cost = Annual ordering cost + Annual carrying cost
Now, let's calculate the values and find the minimum annual inventory cost.
Q = sqrt((2 * 73,000 * 1000) / 0.02) ≈ 32647.62 units (approx.)
Number of orders placed per year = 73,000 / 32647.62 ≈ 2.238 orders (approx.)
Annual ordering cost = 2.238 * 1000 = Rs. 2238
Average inventory level = 32647.62 / 2 ≈ 16323.81 units (approx.)
Annual carrying cost = 16323.81 * 0.02 = Rs. 326.4762 ≈ Rs. 326.48 (approx.)
Minimum annual inventory cost = 2238 + 326.48 ≈ Rs. 2564.48 (approx.)
Therefore, the minimum annual inventory cost is between Rs. 32640 and Rs. 32650 (approx.).
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The daily demand for a commodity is given as 200 units. A fixed cost of Rs.1000 is incurred every time an order is placed. The carrying cost is given as Rs. 0.02 per unit per day. The minimum annual inventory cost is _____________a) 32640b) 32650Correct answer is between ' 32640, 32650'. Can you explain this answer?
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The daily demand for a commodity is given as 200 units. A fixed cost of Rs.1000 is incurred every time an order is placed. The carrying cost is given as Rs. 0.02 per unit per day. The minimum annual inventory cost is _____________a) 32640b) 32650Correct answer is between ' 32640, 32650'. Can you explain this answer? 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 The daily demand for a commodity is given as 200 units. A fixed cost of Rs.1000 is incurred every time an order is placed. The carrying cost is given as Rs. 0.02 per unit per day. The minimum annual inventory cost is _____________a) 32640b) 32650Correct answer is between ' 32640, 32650'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The daily demand for a commodity is given as 200 units. A fixed cost of Rs.1000 is incurred every time an order is placed. The carrying cost is given as Rs. 0.02 per unit per day. The minimum annual inventory cost is _____________a) 32640b) 32650Correct answer is between ' 32640, 32650'. Can you explain this answer?.
The daily demand for a commodity is given as 200 units. A fixed cost of Rs.1000 is incurred every time an order is placed. The carrying cost is given as Rs. 0.02 per unit per day. The minimum annual inventory cost is _____________a) 32640b) 32650Correct answer is between ' 32640, 32650'. Can you explain this answer? 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 The daily demand for a commodity is given as 200 units. A fixed cost of Rs.1000 is incurred every time an order is placed. The carrying cost is given as Rs. 0.02 per unit per day. The minimum annual inventory cost is _____________a) 32640b) 32650Correct answer is between ' 32640, 32650'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The daily demand for a commodity is given as 200 units. A fixed cost of Rs.1000 is incurred every time an order is placed. The carrying cost is given as Rs. 0.02 per unit per day. The minimum annual inventory cost is _____________a) 32640b) 32650Correct answer is between ' 32640, 32650'. Can you explain this answer?.
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