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

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 $4.00 a box. The lettuce is sold for $10 a box, and the dealer that sells the old lettuce is willing to pay $1.50 a box. Past history says that tomorrows demand for lettuce averages 250 boxes with a standard deviation of 34 boxes. How many boxes of lettuce should the supermarket purchase tomorrow?

Explanation / Answer

This is a case of Understocking & overstocking

Given

Cost price = $ 4 /box , Selling price is = $ 10 /box , salvage value = $1.50

Answer

Cu= Cost of understocking = S.P- C.P= $ 10.00 - $4.00 =$ 6

Co = Cost of Over stocking = C.P - Salvage value = $ 4 - $ 1.50 = $ 2.50

P ( D<=Q) = Cu / (Cu+Co) = 6 / (6+2.5) = 0.705

Now , with the help of help of standard normal distribution table we found that the Z value of 0.705 is 0.55

So the super market should purchase = D + (Z value )(standard dev) = 250 + (0.55x34) = 268.7 or 269 boxes of lettuce the supermarket should purchase tomorrow

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