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25 September, 13:37

A restaurant has an annual demand for 882 bottles of California wine. It costs $1 to store 1 bottle for 1 year, and it costs $6 to place a reorder. Find the optimum number of bottles per order.

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  1. 25 September, 17:30
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    73 bottles

    Explanation:

    Let x = total number of orders

    C (x) indicates number of orders and the cost of storage

    Thus,

    6$ dollar to place a reorder

    So,

    C (x) = 1 (882/x) + 6x = 882/x+6x

    C' (x) = -882/x^2+6=0

    6=882/x^2.

    Thus,

    x^2=882/6

    Which indicates 882/12=73 bottles of wine per order

    Thus C (12) = 1*73+6*12=$145 per year

    The best possible number of bottles per order = 73 bottles
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