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The local supermarket buys lettuce each day to ensure really fresh produce. Each

ID: 377924 • 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 $3.00 a box. The lettuce is sold for $14.00 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 235 boxes with a standard deviation of 35 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 $3.00 a box. The lettuce is sold for $14.00 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 235 boxes with a standard deviation of 35 boxes.

Explanation / Answer

Given are following data :

Purchase cost of Lettuce = C = $ 3/ unit

Sale price of Lettuce = P = $14 / unit

Salvage price of old lettuce = S = $1.5 / unit

Therefore ,

Unit cost of underage = Cu = P - C = $14 - $3 = $11

Unit cost of overage = Co = C - S = $ 3 - $1.5 = $1.5

Therefore,

Critical ratio = Cu/ Cu + Co = 11/(11 + 1.5) = 11/12.5 = 0.88

Critical ratio is the probability of optimum demand quantity of tomorrow which will maximize proit.

Corresponding Z value for probability 0.88 = NORMSINC ( 0.88) = 1.174

Therefore , number of boxes of Lettuce supermarket will buy tomorrow

= Mean demand + Z x Standard deviation of demand tomorrow

= 235 + 1.174 x 35

= 235 + 41.09

= 276.09 ( 276 rounded to nearest whole number )

SUPERMARKET SHOULD BUY 276 BOXES OF LETTUCE TOMORROW