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Linear Programming Feed Mix Optimization

This repository contains an academic Operations Research case study focused on solving a feed mix cost optimization problem using Linear Programming and Excel Solver.

The goal of the project is to determine the optimal number of pounds of each ingredient needed to produce a feed mix while satisfying nutritional and supply constraints at the minimum possible cost.

Project Type

Academic / Operations Research / Linear Programming / Decision Support

Problem Overview

The Southfork Feed Company wants to produce a feed mix using four ingredients:

  • Oats
  • Corn
  • Soybeans
  • Vitamin supplement

The company has limited supplies of each ingredient and must meet several nutritional and production requirements. The objective is to minimize the total cost of the final feed mix while satisfying all constraints.

Decision Variables

Let:

  • X1 = pounds of oats
  • X2 = pounds of corn
  • X3 = pounds of soybeans
  • X4 = pounds of vitamin supplement

Objective Function

The objective is to minimize total cost:

Minimize Z = 0.5X1 + 1.2X2 + 0.6X3 + 2.0X4

Constraints

The model includes the following constraints:

  • Oats availability: X1 <= 300
  • Corn availability: X2 <= 400
  • Soybeans availability: X3 <= 200
  • Vitamin supplement availability: X4 <= 100
  • Total mix weight must be at least 500 pounds
  • Soybeans must be at least 30% of the mix
  • Vitamins must be at least 20% of the mix
  • The ratio of corn to oats cannot exceed 2:1
  • The amount of oats cannot be greater than the amount of soybeans
  • Non-negativity constraints for all variables

Solution Method

The problem was modeled as a Linear Programming problem and solved using Microsoft Excel Solver.

The solution process included:

  • Defining decision variables
  • Writing the objective function
  • Translating business requirements into mathematical constraints
  • Building the model in Excel
  • Running Solver to find the minimum-cost solution
  • Reviewing the sensitivity report and final output

Optimal Solution

The optimal feed mix is:

Oats: 200 lb
Corn: 0 lb
Soybeans: 200 lb
Vitamin supplement: 100 lb

Minimum total cost:

$420

Key Result

The optimal solution satisfies all supply, nutritional, and total weight constraints while minimizing the total production cost.

Files

  • Linear_Programming_Feed_Mix_Optimization_Clean.pdf — Clean public version of the case study presentation.

Skills Demonstrated

  • Linear Programming
  • Operations Research
  • Decision Support
  • Mathematical Modeling
  • Optimization
  • Constraint Formulation
  • Excel Solver
  • Sensitivity Analysis
  • Analytical Thinking
  • Academic Presentation

Notes

This project was created for academic learning purposes.

The uploaded PDF is a cleaned public version with personal and team information removed.