• Abhinav Bangia

# pip install PuLP : Getting started with Linear Optimization

### 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 : These are linear restrictions on decisions variables.

### 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

1. Let x be the of medicine A produced and y be the medicine B product in the week

2. Objective Function : Max(z) = 1x + 1.5y

3. Decision Variables (Subject to) 1x + 2y <= 100 (Available Manufacturing Hours) 2x + 1y <=100 ( Available Packaging Hours)

4. Constraints : x >= 0 & y >= 0

### 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.

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