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 $11.00 a box. The lettuce is sold for $24.00 a box and the dealer that sells old lettuce is willing to pay $3.00 a box. Past history says that tomorrow's demand for lettuce averages 275 boxes with a standard deviation of 45 boxes.

a. How many boxes of lettuce should the supermarket purchase tomorrow? (Use Excel's NORM.S.INV() function or z-table to find the z value. Round your answer to the nearest whole number)

Multi-period Model- Fixed-Time Period Model (P-model)

Answer 1

Co = buying price – discard price = 11.00 – 3.00 = 8.00

Cu = selling price – buying price = 24.00 − 11.00 = 13.00.

Let us calculate the Newsvendor fractile using the formula p = Cu/(Cu + Co)

p = (Cu/(Cu + Co))*100% = (13.00 / (13.00 + 8.00)) * 100% = (13.00 / 21.00) * 100% = 0.6190 * 100 = 61.90%

The corresponding z value using Norm.s.inv() = 0.3028

So, the optimal quantity is Q = Demand + std dev * z = 275 + (45 * 0.3028) = 275 + 13.626 = 288.626 = 289 boxes

Answer: The supermarket must buy 289 boxes of lettuce for tomorrow