Question

Daily production capacity of a bearing manufacturing company is 30000 bearings. The daily demand of the bearing is 15000. The holding cost per year of keeping a bearing in the inventory is ₹ 20. The setup cost for the production of a batch is ₹ 1800. Assuming 300 working days in a year, the economic batch quantity in number of bearings is \(\underline{\hspace{1cm}}\) (in integer).

Hint:

The economic batch quantity (EBQ) minimizes the total cost of inventory and production by balancing the setup and holding costs.

Answer 1

Correct Answer: 40200 - 40300

To determine the economic batch quantity (EBQ) for the bearing manufacturing company, we'll use the Economic Production Quantity (EPQ) formula. The formula for EPQ is given by:

\(EPQ = \sqrt{\frac{2DS}{H} \cdot \frac{P}{P-D}}\)

where:

• \(D\) = Annual demand = \(15,000 \text{ bearings/day} \times 300 \text{ days} = 4,500,000 \text{ bearings/year}\)
• \(S\) = Setup cost per batch = ₹1800
• \(H\) = Holding cost per bearing per year = ₹20
• \(P\) = Production rate per day = 30,000 bearings

Substitute the values into the formula:

\(EPQ = \sqrt{\frac{2 \times 4,500,000 \times 1800}{20} \cdot \frac{30,000}{30,000 - 15,000}}\)

Perform the calculations:

• First, calculate \( \frac{2 \times 4,500,000 \times 1800}{20} = \frac{16,200,000,000}{20} = 810,000,000\)
• Calculate \( \frac{30,000}{15,000} = 2\)
• Therefore, multiply: \(810,000,000 \times 2 = 1,620,000,000\)
• Now take the square root: \(\sqrt{1,620,000,000} \approx 40200\)

Thus, the economic batch quantity is 40,200 bearings.