Carly's Creative is a leather goods store that produces three items shoes, belts and wallets. Carly wants to make the most profit she could make. She defines profit as her total revenues form sales minus her total cost of resources. The production of all three items require the same three limited resources: leather, metal and labor but in different quantities as indicated below
Shoes (a pair) require 10 oz of leather 2 oz of metal and 3 hours of labor
Belts require 6 oz of leather; 3 oz of metal and 1 hour of labor
Wallets require 3 oz of leather, 1 oz of metal and 2 hours of labor
Shoes can be sold for $50 a pair. Belts can be sold for $30 each. Wallets can be sold for $25 each. Regardless of what item the resource is used for leather cost $ 2 per ounce, metal costs $1 pr ounce and labor cost $7 per hour
Because the three resources are limited she has 5,000 ounces of leather, 3,000 ounces of metal and 2,500 hours of labor - it is important to calculate how much resource is used, show it in a spreadsheet
a) What is her objective?
b) What are her constraints?
c) What are her decision variables?
d) Draw an influence chart with mathematical operators for this problem using the term: Profit, Revenue, Total cost of resources, Cost of Leather, Cost of Metal, Cost of Labor, Leather per unit, unit cost of leather, unit cost of metal, unit cost of labor, leather used, metal used, labor used, unit selling price, quantity.
e) Spreadsheet - enter in each cell either a formula or a fixed number, based upon the information provided (only cells that have "meaning" should contain formulas in the "total " column
f) If you can program the spreadsheet using WhatsBest or Solver software.
1. What is her objective?
Her objective is to maximize profits by choosing a mix so that she can create the maximum difference between her revenues and total costs.
2. What are her constraints?
Her constraints are the total amount of resources that can be used. These are 5,000 ounces of leather, ...
This solution explains determining mathematically the objective, constraints and variables when attempting to maximize profit for a case study of a leather goods store. It also explains how to draw an influence chart on a spreadsheet.