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 $4.00 a box. The lettuce is sold for $10.00 a box and the dealer that sells old lettuce is willing to pay $1.50 a box. Past history says that tomorrow's demand for lettuce averages 250 boxes with a standard deviation of 34 boxes. How many boxes of lettuce should the supermarket purchase tomorrow? (Use Excel's NORMSINV) 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 boxes

Explanation / Answer

Underage cost, Cu = selling price - cost = 10 - 4 = 6

Overage cost, Co = cost - salvage value = 4 - 1.5 = 2.5

Optimal service level to maximize profit () = Cu/(Cu+Co) = 6/(6+2.5) = 0.706

z-statistic = NORMSINV(0.706) = 0.5414

Mean demand, = 250 boxes

Std dev of demand, = 34 boxes

Number of boxes = + z = 250 + 0.5414*34 = 268 boxes

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