The local supermarket buys lettuce each day to ensure really fresh produce. Each
ID: 470361 • 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 $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? (Round your answer to the nearest whole number.)
Explanation / Answer
Purchase cost = $4.00 per box
Selling price = $16.00 per box
Salvage value = $2.50 per box
Mean demand = µ =252 boxes
Standard Deviation = = 34 boxes
For the given data apply single-period Inventory model (Newsvendor Problem)
Cs = cost of shortage (underestimate demand) = Sales price/unit – Cost/unit
Co = Cost of overage (overestimate demand) = Cost/unit – Salvage value /unit
Cs = 16.00 – 4.00 = $12.00 per box
Co = 4.00 – 2.50 = $1.50 per box
The service level or probability of not stocking out, is set at,
Service Level = Cs/( Cs + Co) = 12/(12 + 1.50)
Service Level = 0.89
Supermarket owner needs to find the Z socre for the demand normal distribution that yields a probability of 0.8889.
So 88.89% of the area under the normal curve must be to the right of the optimal stocking level.
Using standard normal table, for an area of 0.8889, the Z score is 1.2207.
Optimal order quantity = µ + z = 252 + (1.2207)34
Optimal order quantity = 293.5038 boxes or 294 boxss
Cynthia should order 294 boxes of lettuce for tomorrow.
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