In: Operations Management
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.)
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: