Explanation Given: Q = 2 × 10 6 gal d = $ 8000 s = 30 cent/gal-yr Calculation: Let, N be the number of shipments per year so that the time interval between the shipments is T = 1 N years. Therefore, the total storage costs will be T = s Q N . The delivery cost per year is d N The total cost is given by C ( N ) = s Q N + d N On solving this equation, we obtain C ' ( N ) = − s Q N 2 + d = 0 On solving this equation, we obtain N = ( s

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Author: Rogawski

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Chapter 4.6, Problem 64E

To determine

To show that the costs are minimized for N=(sQd) and to find theoptimum number of deliveries.

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Chapter 4.6, Problem 63E

Chapter 4.6, Problem 65E

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Chapter 4 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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To show that the costs are minimized for N = ( s Q d ) and to find theoptimum number of deliveries.

Solution Summary: The author calculates that the optimum number of deliveries per year is 9. The time interval between shipments is T=1N years.

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To show that the costs are minimized for N=(sQd) and to find theoptimum number of deliveries.

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Chapter 4 Solutions