Problem 10-13 (Algorithmic) Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7,800 copies. The cost of one copy of the book is $13.5. The holding cost is based on an 17% annual rate, and production setup costs are $135 per setup. The equipment on which the book is produced has an annual production volume of 26,000 copies. Wilson has 250 working days per year, and the lead time for a production run is 14 days. Use the production lot size model to compute the following values: Minimum cost production lot size. Round your answer to the nearest whole number. Do not round intermediate values.

The minimum cost production lot size = 2447.75

Explanation:

Given

D = Demand = 7,800 copies.

C = Setup costs = $135 per setup.

A = Cost = $13.5.

R = Holding Cost Annual Rate = 17%

P = Production volume = 26,000 copies.

W = Working days = 250 per year

L = Lead time for a production run = 14 days

First we calculate the usage rate.

The usage rate = Annual rate of demand ÷ Working days

Usage Rate = 7500 ÷ 250 = 30 units daily

Then we calculate the production units

Production (P) = Annual Production Volume ÷ Working days

P = 26000 ÷ 250 = 104 units daily

Then we calculate the cost production lot size

This is calculated by

Cost production lot size = √(2DC)/√(1 - (D/P)R * A)

By substituton

Cost Production = √(2 * 7500 * 135)/√(1 - (7500/26000) * 0.17 * 13.5)

Cost Production = 2447.746953702503

Hence, the minimum cost production lot size = 2447.75 --- Approximately

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