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 $6.00 a box. The lettuce is sold for $18.00 a box and the dealer that sells old lettuce is willing to pay $3.60 a box. Past history says that tomorrow's demand for lettuce averages 254 boxes with a standard deviation of 37 boxes. How many boxes of lettuce should the supermarket purchase tomorrow? (Use Excel's NORMSINV() function to find the Z-score. Round intermediate calculations to four decimal places. Round your answer to the nearest whole number.) Number of boxes

Answer 1

289 boxes

Step-by-step explanation:

Calculation to determine How many boxes of lettuce should the supermarket purchase tomorrow

First step is to calculate Co using this formula

Co = buying price – discard price

Let plug in the formula

Co= 6.00 – 3.60

Co =2.40

Second step is to calculate Cu using this formula

Cu = selling price – buying price

Let plug in the formula

Cu= 18.00 − 6.00

Cu= 12.00

Third step is to calculate the Newsvendor fractile

using the formula this formula

p = Cu/(Cu + Co)

Let plug in the formula

p = (Cu/(Cu + Co))*100%

p= (12.00 / (12.00 + 2.40)) * 100%

p= (12.00 / 14.40) * 100%

p= 0.83 * 100

p= 83%

Fourth Step is to find the corresponding z value using Norm.s.inv() which gives us 0.954

Now let calculate the optimal quantity

Using this formula

Optimal quantity (Q) = Demand + std dev * z

Let plug in the formula

Q= 254 + (37* 0.954)

Q= 254+ + 35.298

Q= 289.298

Q= 289 boxes (Approximately)

Therefore How many boxes of lettuce should the supermarket purchase tomorrow is 289 boxes