- Abhinav Bangia

# pip install PuLP : Getting started with Linear Optimization

*Understanding Linear Programming*

*Understanding Linear Programming*

Linear programming (LP) is a method for engineers or data scientists to find the best outcome of a business problem i.e maximum profit, minimum cost in a linear mathematical model.

Each of the LP problem consist of following components :

**1. Objective Function :**Purpose behind LP i.e maximize profit, minimize loss ,**2. Decision Variables :**These are the controllable variables that influence the objective function,**3. Constraints :**

*Case Example : XYZ Pharmaceuticals *

*Case Example : XYZ Pharmaceuticals*

XYZ Pharmaceuticals manufacturers two types of medicine with same salt : A and B. The manufacturer wants to maximize their weekly operational profit.

$1 of profit per medicine A.

$1.5 of profit per medicine B.

Medicine A requires 1 hour of manufacturing labor and 2 hours of packaging labor.

Medicine B requires 2 hours of manufacturing labor and 1 hour of packaging labor.

Each week, XYZ has only 100 hours of manufacturing labor and 100 hours of packaging labor available.

*Lets Build the Objective Function, Decision Variables and Constraints*

*Lets Build the Objective Function, Decision Variables and Constraints*

Let

**x**be the of medicine A produced and**y**be the medicine B product in the week**Objective Function :**Max(z) = 1x + 1.5y**Decision Variables (Subject to)**1x + 2y <= 100 (Available Manufacturing Hours) 2x + 1y <=100 ( Available Packaging Hours)**Constraints :**x >= 0 & y >= 0

*Loading & Solving the Problem Statement in PuLP*

*Loading & Solving the Problem Statement in PuLP*

**Discussing Solution**

**Discussing Solution**

*We see that the optimal solution for production of Medicine A & B to return maximum profit is 33.33 units weekly for both A & B to maximize the profit up to 83.33 units. We can even plot the illustrative graph using matplotlib library in python. *

There are many commercial optimizer tools, but having hands-on experience with a programmatic way of doing optimization is invaluable.