The local supermarket buys lettuce each day to ensure really fresh produce. Each
ID: 375170 • Letter: T
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 $11.00 a box. The lettuce is sold for $25.00 a box and the dealer that sells old lettuce is willing to pay $3.00 a box. Past history says that tomorrow's demand for lettuce averages 265 boxes with a standard deviation of 42 boxes.
How many boxes of lettuce should the supermarket purchase tomorrow? (Use Excel's NORMSINV() function to find the Z-score. Round intermediate calculations to four decimal places. Round your answer to the nearest whole number.)
Number of boxes > .............
Explanation / Answer
Cost of shortage = Cu = Selling price- Cost price = 25 – 11 = 14 $
Cost of overstock = Co= Cost price – salvage price = 11 – 3 = 8 $
Probability = Cu/(Co+Cu) = 14/22 = .6363
Z-score for .6363 probability = .34858 = .3486
Supermarket should purchase = 265 + .3486*42 = 279.64 = 280 boxes
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