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Mathematics - Calculus - Minimizing Cost

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An electronic firm uses 600 cases of transistors each year. Each case costs $1000. The cost of storing one case for a year is 90 cents and the ordering fee is $30 per shipment. How many cases should the firm order each time to keep total cost at minimum. (Assume that transistors are use at a constant rate throughout the year and that each shipment arrives just as the preceeding shipment is being used up.

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The expert uses calculus to determine minimizing costs. A complete, neat and step-by-step solution is provided.

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Let the firm order x cases each time.

Total cost = fixed cost + variable cost = [600 x 1000] + ...

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