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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?

Short Answer

Expert verified

Anything resembles a supermarket, particularly in terms of the range or quantity of its goods or services

Step by step solution

01

Given

Cost of box =$ 4

Selling price of per box = $ 10

Selling price of old product = $ 1.50

Average demand = 250 boxes

Standard deviation = 34 boxes

02

Service Level

Excess cost per boxCe=Cost of the per box-Selling price of old boxesCe=$4-$1.50Ce=$2.50

Shortage cost per boxCs=Selling price of the per box-cost price of boxesCs=$10-$4Cs=$6

Service level =CSCS-Ce=66 + 2.5= 0.70589

03

Find the Z score using the = NORMSINV() function in the excel spreadsheet

Calculation of Optimal stock level:-

Optimal Stocking levelSo=²Ñ±ð²¹²Ô+³úσSo=250+0.541417×34So=268.4 or 268 approx

As a result, the supermarket should buy 268 boxes oflettuce tomorrow.

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