Chapter 4: Q. 4OQ (page 544)

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?

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

Step by step solution

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

$Excess cost per box (C_{e}) =Cost of the per box - Selling price of old boxes (C_{e}) = $ 4 - $ 1.50 (C_{e}) = $ 2.50$

$Shortage cost per box (C_{s}) =Selling price of the per box - cost price of boxes (C_{s}) = $ 10 - $ 4 (C_{s}) = $ 6$

$Service level = \frac{C_{S}}{C_{S} - C_{e}} = \frac{6}{6 + 2.5} = 0.70589$

Calculation of Optimal stock level:-

$Optimal Stocking level (S_{o}) =Mean+zσ (S_{o}) = 250 + 0.541417 \times 34 (S_{o}) = 2 68.4 or 268 approx$

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

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