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4 December, 15:42

Skinner's Fish Market buys fresh Boston bluefish daily for $4.20 per pound and sells it for $5.70 per pound. At the end of each business day, any remaining bluefish is sold to a producer of cat food for $2.40 per pound. Daily demand can be approximated by a normal distribution with a mean of 80 pounds and a standard deviation of 10 pounds. What is the optimal stocking level?

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  1. 4 December, 15:47
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    optimal stocking level is 78.9 pound

    Explanation:

    Given data

    buys = $4.20

    sell = $5.70

    sold = $2.40

    mean = 80

    standard deviation = 10

    to find out

    optimal stocking level

    solution

    we know here profit is = 5.70 - 4.20 = 1.50

    profit = $1.50

    loss = 4.20 - 2.40 = 1.80

    loss = $1.80

    so here

    Critical Ratio = profit / (profit + loss)

    Critical Ratio = 1.5 / (1.5 + 1.8)

    Critical Ratio = 0.4545

    so now from excel using the Norm. Inv we get Z

    Z value (=NORM. INV (0.4545,80,10)

    for mean 80 and SD = 10

    the value of Z = - 0.11

    so

    optimal stocking level = mean + Z (SD)

    optimal stocking level = 80 + (-0.11) (10)

    optimal stocking level is 78.9 pound
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