Problem 20-4 The local supermarket buys lettuce each day to ensure really fresh

Question

Problem 20-4 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 $7.00 a box. The lettuce is sold for $16.00 a box and the dealer that sells old lettuce is willing to pay $4.00 a box. Past history says that tomorrow's demand for lettuce averages 272 boxes with a standard deviation of 48 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 boxes

Explanation / Answer

cost of underestimating demand cu = 16 -7 = 9

cost of overestimating demand co = 7 - 4 = 3

optimal probability of lettuce not being sold denoted by P

P >= cu/co+cu

= 9/3+9

= 0.75

z = NORMSINV(0.75) = 0.67

number of boxes = average demand of boxes + value of z * standard deviation

= 272 + 0.67 * 48

= 304.16

hence the supermarket should purchase 304 boxes

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