the local supermarket buys lettuce each day to ensure really fresh produce. Each

Question

the local supermarket buys lettuce each day to ensure really fresh produce. Each morning any lettuce that is left from the previous day is sold to a dealer that resells it to farmers who use it to feed their animals. This week the supermarket can buy fresh lettuce for $4 a box. Each box contains 10 heads of lettuce. The lettuce is sold for $1 a head and the dealer that sells old lettuce is willing to pay $0.20 per head. Past history says that tomorrow’s demand for lettuce averages 2500 heads with a standard deviation of 750 heads. How many boxes should the supermarket purchase tomorrow? (A fractional answer is okay). Please write full answer with details.

Explanation / Answer

The newsvendor fractile, p = Cu/(Cu + Co)

where Co = 4 - 0.20 = 3.8, Cu = 10 x (1 Dollar) - 4 = 6

So p = 6/9.8 = 70.59%

Then, the optimal quantity is Q = 2500 + 750 x z, where the corresponding z value is z = 0.54,

so Q = 2500 + 750 x 0.54 = 2905

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