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4 October, 10:50

A local farm market buys fresh fruits and vegetables from local farmers. It buys peaches from one farmer at a cost of $1.00 per pound and sells them for $2.00 per pound. The demand for peaches during the season is normally distributed with a mean of 40 pounds per day and a daily standard deviation of 6 pounds. At the end of each business day, any unsold peaches are purchased by local restaurants for $0.40 per pound (in U. S. dollars) : Enter your answers to one decimal place. Determine the service level. The service level is Number %. What is the optimal stocking level for the service level deterimined in (a)

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  1. 4 October, 11:14
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    1. The service level is 63%

    2. 42 pounds

    Explanation:

    1. Cost Price of Peaches = $1.00 per pound

    Selling Price of Peaches = $2.00 per pound

    Cost of shortage = Selling Price of Peaches - Cost Price of Peaches = $2 - $1 = $1

    Cost of overage = Cost Price of Peaches - salvage value = $1 - $0.4 = $0.6

    Service level = Cost of shortage / (Cost of shortage + Cost of overage)

    = $1 / ($1 + $0.6) = $1/$1.6 = 0.625 = 62.5% ≈ 63%

    The service level is 63%

    2. The z value for this service level = 0.332

    Mean = 40 pounds

    Standard deviation = 6 pounds

    Optimum stocking level = (Mean + z value x Standard deviation)

    = 40 + 6 * 0.332 = 41.992 ≈ 42 pounds

    The optimal stocking level for the service level deterimined in (a) is 42 pounds
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