The local supermarket buys lettuce each day to ensure really fresh produce. Each
ID: 450608 • 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 NORMSINV() function to find the correct critical value for the given -level. Do not round intermediate calculations. Round your answer to the nearest whole number.)
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.
Explanation / Answer
U = Cost of Shortage (Stock out or lost sale) = $16 - $8 = $8.00
O = Cost of overage (Overstock) = $8 - $1.80 = $6.2
P less than equal to U/(U + O) = 0.5634
From Z- table (Normal Curve) For Probability 0.5634 , Z value is 0.16
Therefore the supermarket should purchase 245 + 0.16 (38) = 251.08 or 252 boxes of lettuce
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