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 \(4.00 a box. The lettuce is sold for \)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. How many boxes of lettuce should the supermarket purchase tomorrow?

Short answer

Anything resembles a supermarket, particularly in terms of the range or quantity of its goods or services

Step-by-step solution

Given

Cost of box =$ 4

Selling price of per box = $ 10

Selling price of old product = $ 1.50

Average demand = 250 boxes

Standard deviation = 34 boxes

Service Level

$$\begin{gathered} \text{Excess cost per box}\left({\text{C}}_{\text{e}}\right)\text{=Cost of the per box}-\text{Selling price of old boxes} \\ \left({\text{C}}_{\text{e}}\right)=\$4-\$1.50 \\ \left({\text{C}}_{\text{e}}\right)=\$2.50 \end{gathered}$$

$$\begin{gathered} \text{Shortage cost per box}\left({\text{C}}_{\text{s}}\right)\text{=Selling price of the per box}-\text{cost price of boxes} \\ \left({\text{C}}_{\text{s}}\right)=\$10-\$4 \\ \left({\text{C}}_{\text{s}}\right)=\$6 \end{gathered}$$

$$\begin{gathered} \text{Service level =}\frac{{\text{C}}_{\text{S}}}{{\text{C}}_{\text{S}}-{\text{C}}_{\text{e}}} \\ \text{=}\frac{\text{6}}{\text{6 + 2.5}} \\ \text{= 0.70589} \end{gathered}$$

Find the Z score using the = NORMSINV() function in the excel spreadsheet

Calculation of Optimal stock level:-

$$\begin{gathered} \text{Optimal Stocking level}\left({\text{S}}_{\text{o}}\right)\text{=Mean+zσ} \\ \left({\text{S}}_{\text{o}}\right)=250+0.541417\times 34 \\ \left({\text{S}}_{\text{o}}\right)=2\text{68.4 or 268 approx} \end{gathered}$$

As a result, the supermarket should buy 268 boxes oflettuce tomorrow.