The local supermarket buys lettuce each day to ensure really fresh produce. Each
ID: 350878 • 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 Z-score. Round intermediate calculations to four decimal places. Round your answer to the nearest whole number.)
Explanation / Answer
Given are following data :
Sales price of lettuce = P = $ 14 per box
Purchase price of Lettuce = C = $ 3 per box
Salvage price of Lettuce = S = $1.5 per box
Basis above data ,
Cost of underage = Cu = P – C = $14 - $ 3 = $11
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 purchase quantity .
Therefore , probability of optimum purchase quantity = 0.88
Corresponding Z value for probability 0.88 = NORMSINV ( 0.88) = 1.1749
Given are following details :
Tomorrow’s demand for Lettuce = D = 235 boxes
Standard deviation of demand = Sd = 35 boxes
Number of boxes of Lettuce the supermarket should purchase tomorrow
= D + Zx Sd
= 235 + 1.1749 x 35
= 235 + 41.121
= 276.12 ( 276 rounded to nearest whole number )
SUPERMARKET SHOULD PURCHASE 276 BOXES OF LETTUCE TOMORROW
SUPERMARKET SHOULD PURCHASE 276 BOXES OF LETTUCE TOMORROW
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.