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 $10.00 a box. The lettuce is sold for $21.00 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 262 boxes with a standard deviation of 43 boxes. How many boxes of lettuce should the supermarket purchase tomorrow

Answer 1

Given Information:

Cost price of lettuce = $10

Selling price of lettuce = $21

Salvage value = $2

Average demand of lettuce = μ = 262 boxes

Standard deviation of lettuce = σ = 43 boxes

Required Information:

How many boxes of lettuce should the supermarket purchase = ?

Answer:

n = 271 boxes

Explanation:

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

n = μ + (z-score)σ

Where μ is the average demand of lettuce boxes, σ is the standard deviation, and z-score can be calculated by

p = C_us/(C_us + C_os)

Where the cost of under stocking is given by

C_us = Selling price of lettuce - Cost price of lettuce

C_us = $21 - $10

C_us = $11

The cost of over stocking is given by

C_os = Cost price of lettuce - Salvage value

C_os = $10 - $2

C_os = $8

p = C_us/(C_us + C_os)

p = 11/(11 + 8)

p ≈ 58%

The z-score corresponding to 58% is 0.202

n = 262 + (0.202)43

n = 270.68

n = 271 boxes

Therefore, the supermarket should purchase 271 boxes of lettuce tomorrow.