Question

Optimal lot size =(2SQ/b)¹/²

Where S= setup or order costs Q= Quantity needed B= storage or inventory cost per unit Use the OLS equation to solve the following" Joe's Sandwich Shop uses 40 heads of lettuce per week to make sandwiches. It costs $1 in gas and employee wages for each trip to the farmer's market to purchase lettuce. Storing lettuce in Joe's Sandwich Shop electric cooler costs $0.20 per week per head of lettuce.
1. What is the optimal number of lettuce heads that should be purchased for each trip to the Farmer's market?

Answer 1

The optimal lot size for Joe's Sandwich Shop is 20 heads of lettuce per trip to the farmer's market, which minimizes the sum of setup costs and storage costs.

Step-by-step explanation:

The question asks how to calculate the optimal lot size for purchasing lettuce heads using the given formula: Optimal lot size = √(2SQ/b). In Joe's Sandwich Shop's case, the setup or order cost (S) is $1 for each trip to the farmer's market. The quantity needed (Q) is 40 heads of lettuce per week, and the storage or inventory cost per unit (storage cost, B) is $0.20 per week per head of lettuce.

To find the optimal number of lettuce heads that should be purchased for each trip to the Farmer's market, we substitute the given values into the formula:

Optimal lot size = √((2 * 1 * 40) / 0.20)

This calculates to:

Optimal lot size = √(80 / 0.20) = √400 = 20

Therefore, Joe's Sandwich Shop should purchase 20 heads of lettuce on each trip to the farmer's market to minimize costs, maintaining the balance between ordering costs and holding costs.