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 = ?
Answer:
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.
" ; 
= 53 ÷ 8 = " 6 