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 $10.00 a box and the dealer that sells old lettuce is willing to pay $1.50 a box. Past history says that tomorrow's demand for lettuce averages 250 boxes with a standard deviation of 34 boxes. Required: How many boxes of lettuce should the supermarket purchase tomorrow

Given Information:

Cost price = $4

Selling price = $10

Salvage value = $1.50

Average demand = μ = 250 boxes

Standard deviation = σ = 34 boxes

Required Information:

Number of lettuce boxes = ?

The supermarket should purchase 268 boxes  of lettuce

Step-by-step explanation:

The required number of lettuce boxes that supermarket should purchase is given by

Number of lettuce boxes = μ + (z*σ)

Where μ is the average demand of lettuce boxes, σ is the standard deviation, and z is the z-score which is given by

p = C_us/(C_us + C_os)

The z-score corresponding to probability p will be obtained.

The cost of under stocking is given by

C_us = Selling price - Cost price

C_us = $10 - $4

C_us = $6

The cost of over stocking is given by

C_os = Cost price - Salvage value

C_os = $4 - $1.50

C_os = $2.50

p = C_us/(C_us + C_os)

p = 6/(6 + 2.50)

p = 0.7058

p  = 70.58%

The z-score corresponding to 70.58% probability is approximately 0.54

Number of lettuce boxes = μ + (z*σ)

Number of lettuce boxes = 250 + (0.54*34)

Number of lettuce boxes = 250 + (18.36)

Number of lettuce boxes = 268.36

Number of lettuce boxes ≈ 268

Therefore, the supermarket should purchase 268 boxes of lettuce.

How to use z-table?

Step 1:

In the z-table, find the probability you are looking for and note down the two-digit number of the given row. (e.g 0.5, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table and note down the value in the column for the remaining decimal point in the range of 0.00 to 0.09.

Step 3:

Finally, add the numbers obtained from step 1 and step 2.