A producer of electronic parts wants to take account of both production rate and demand rate in deciding on its lot sizes. A par

Question

2 months ago

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A producer of electronic parts wants to take account of both production rate and demand rate in deciding on its lot sizes. A par

ticular $50 part can be produced at a rate of 100 units per day, and the demand rate is 20 units per day. Assuming there are 300 days in a year. The firm uses a carrying charge of 24% a year, and the setup cost is $200 each time the part is produced.
Required:
a. What lot size should be produced?b. If the production rate is ignored, what would the lot size be? How much does this smaller lot size cost the firm on an annual basis?

Business

1 answer:

arsen [3.4K] · Answer 1 · 2026-04-08T20:50:29+03:00

a) The ideal lot size is 1,118.03. b) The total annual cost adds up to $46.51. Explanation: Based on the information provided, a) The daily holding expense is calculated as $50 × 24% ÷ 300, resulting in $0.04. The optimal lot size is derived from the formula Sqrt(2 × Demand rate × Setup cost ÷ (Daily holding cost × (1 - Demand rate ÷ Production cost))). Inserting values gives us Sqrt(2 × 100 × $200 ÷ ($0.04 × (1 - 20 ÷ 100))) = $1,118.03. b) Ignoring the production rate yields an optimal lot size of Sqrt(2 × 20 × $200 ÷ 1) = 89.44. The annual total cost comprises both setup and holding costs, leading to the result $46.51.