1. The local supermarket buys lettuce each day to ensure really fresh produce. E
ID: 367200 • Letter: 1
Question
1. 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 $16.00 a box and the dealer that sells old lettuce is willing to pay $2.50 a box. Past history says that tomorrow's demand for lettuce averages 252 boxes with a standard deviation of 34 boxes.
How many boxes of lettuce should the supermarket purchase tomorrow?
Explanation / Answer
Let,
Cu = Cost per unit of Demand overestimated
Co = Cost per unit of demand underestimated
Here as per the mentioned details in the question,
Cu = Cost of purchasing the lettuce - Salvage value of Old lettuce
= 4.00 - 2.50
= 1.50
Co = Value of fresh lettuce - Cost of fresh Lettuce
= 16.00 - 4.00
= 12.00
P is the cumulative probability that 1 unit will be sold.
P=Cu/(Cu+Co) = 12.00/(12.00+1.50) = 88.89%
Assuming normal distribution ( Bell Curve ) p value of 88.89% corresponds to z value of 1.220635
Standard deviation = 34 (given)
Order quantity Q = Mean + ( Standard deviation * Z value )
= 252 + (34*1.220635)
= 252 + 41.50159
= 293.5 or approximated to 294.
So the super market should purchase 294 boxes of lettuce tomorrow. :-)
Happy learning :-)
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