The local supermarket buys lettuce each day to ensure really fresh produce. Each
ID: 361539 • 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 $8.00 a box. The lettuce is sold for $16.00 a box and the dealer that sells old lettuce is willing to pay $1.80 a box. Past history says that tomorrow's demand for lettuce averages 245 boxes with a standard deviation of 38 boxes. How many boxes of lettuce should the supermarket purchase tomorrow? (Use Excel's NORMSINVO) function to find the correct critical value for the given a-level. Do not round intermediate calculations. Round your answer to the nearest whole number.) Number of boxesExplanation / Answer
Cost of shortage (Cs) = Selling price - Cost price = 16 - 8 = 8$
Cost of excess (Ce) = Cost price - Salvage cost = 8 - 1.8 = 6.2$
Mean = 245
Standard deviation = 38
Service level = Cs/(Cs+Ce) = 8/(8+6.2) = 0.56
Optimal stocking = Mean + z*standard deviation
z for Service level 0.56 is 0.15 (Using NORMSINV function)
Optimal Stocking = 245 + 0.15*38 = 250.7
Hence, 251 boxes
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