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7 November, 18:55

A manufacturer of industrial sales has production capacity of 1,000 units per day. Currently, the firm sells production capacity for $10 per unit. At this price, all production capacity gets booked about one week in advance. A group of customers have said that they would be willing to pay $15 per unit if capacity was available on the last day. About ten days in advance, demand for the high-price segment is normally distributed with a mean of 250 and a standard deviation of 100. How much production capacity should the manufacturer reserve for the last day

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  1. 7 November, 19:13
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    The production capacity the manufacturer should reserve for the last day = 206.00 units.

    Explanation:

    Normal production = 1000 X $ 10

    Normal production = $ 10,000

    Spot production = 1,000 X $ 15

    Spot production = $ 15,000

    p * = 15,000 - 10,000 / 15,000

    p * = 0.33

    Q = norminv (0.33,250,100)

    The production capacity the manufacturer should reserve for the last day = 206.00 units
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