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26 January, 21:14

consider a product meeting the newsvendor assumptions. The unit purchase cost is $140. For each sold unit, you earn a profit of $60. For each leftover, you lose $30. The demand follows a normal distribution with a mean 80 and a standard deviation 30. Calculate the newsvendor critical ratio. what is the optimal order quantity

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  1. 26 January, 21:34
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    Newsvendor critical ratio = 0.35

    Optimal quantity = 92.6 units

    Explanation:

    Cost = $140

    Profit = $60

    Loss = $30

    Mean = 80

    S. D = 30

    Revenue = cost + profit

    = 140 + 60

    = $200

    Cost of under stock = revenue - cost

    = 200 - 140

    = $60

    Cost of over stock = cost - salvage value

    = 140 - 30

    = $110

    The newsvendor critical ratio is calculated using the formula;

    newsvendor critical ratio=

    Cost of under stock/Cost of under stock + Cost of over stock

    Newsvendor critical ratio = 60 / (60 + 110)

    = 60/170

    = 0.35

    z = 0.3853

    Optical quantity is given as;

    Q = 80 + 0.3853 * 30

    = 92.6 units
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