To determine To find: The optimum number of copies per order minimizes the annual cost. Explanation Formula used: The number production in each batch is q = 2 f M k . The total cost is T ( q ) = f M q + k q 2 . The number of batches per year is M q . Here, k be the cost of storing one unit of the product for one year, f be the fixed setup cost to manufacture the product, g be the cost of manufacturing a single unit of the product and M be the total number of units produced annually then Calculation: The annual demand of a bookstore is M = 100 , 000 . The cost to store 1 copy for 1 year is k = 0.50 . The fixed cost is f = 60 . Compute the optimum number of copies per order minimizes the annual cost. Substitute k = 0.50 , M = 100 , 000 and f = 60 in q = 2 f M k , q = 2 × 60 × 100 , 000 0.50 = 12 , 000 , 000 0.50 = 24,000,000 ≈ 4898.98 Thus, the optimum number of copies per order minimizes the annual cost is about q ≈ 4898.98 . Check for more accuracy by taking q = 4898 and q = 4899 then compare which total cost is minimum. Substitute q = 4898 , k = 0

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 6.3, Problem 13E

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To find: The optimum number of copies per order minimizes the annual cost.

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Chapter 6.3, Problem 12E

Chapter 6.3, Problem 14E

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Calculus with Applications (11th Edition)

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