Question

In: Operations Management

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

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 $7.00 a box. The lettuce is sold for $18.00 a box and the dealer that sells old lettuce is willing to pay $2.00 a box. Past history says that tomorrow's demand for lettuce averages 255 boxes with a standard deviation of 40 boxes.

How many boxes of lettuce should the supermarket purchase tomorrow? (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Do not round intermediate calculations. Round your answer to the nearest whole number.)

Expert Solution

Answer: 275 boxes

Explanation:

Buying Price (C) = $ 7.00 per box

Selling Price (P) = $ 18.00 per box

Salvaging Value = Price paid by dealer for old lettuce = $2

Now, we need to find the Cost of Under stocking and Cost of Overstocking to calculate Critical Ratio

Cost of Under stocking (Cu) = Selling Price - Buying Price = 18 - 7 =$11

Cost of Overstocking (Co) = Buying Price - Salvaging Value = 7 -2 = $5

Critical Ratio = Cu / (Cu + Co) = 11 / (11 + 5) = 0.6875

This is the probability on Normal Distribution Curve to maximize the profit

Market Demand is normally Distributed with mean 255 and std deviation of 40

Purchase qty = NORMINV ( Critical Ratio, Mean, Std Deviation 0 = 274.55 ~ 275

Supermarket should purchase 275 boxes of lettuce for tomorrow

Excel:

keosha answered 1 month ago

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