Solving LPs in Python with pulp

Linear programming (LP) problems frequently appear in analytics when you want to optimize an objective—such as minimizing costs or maximizing profit—while satisfying real-world constraints. Python’s PuLP library provides a simple and intuitive way to formulate and solve LPs without requiring any low-level solver knowledge.

What Is PuLP?

PuLP is a Python library that allows you to create optimization problems in a readable, model-oriented way. It automatically connects to solvers such as CBC (default), GLPK, or commercial ones if available.

Working with PuLP usually involves:

• Defining a problem object
• Declaring decision variables
• Writing the objective function
• Adding constraints
• Solving the model and retrieving the results

Basic Structure of an LP in PuLP

Below is the general template of an LP model:

# 1. Create problem
problem = LpProblem("My_Problem", LpMinimize)  # or LpMaximize

# 2. Create variables
x = LpVariable("x", lowBound=0)
y = LpVariable("y", lowBound=0)

# 3. Objective function
problem += 3*x + 5*y

# 4. Constraints
problem += x + 2*y <= 10
problem += 3*x + y <= 12

# 5. Solve
problem.solve()

Example: Resource Allocation Problem

Suppose a company produces two products using limited machine hours.

• Product A requires 2 hours
• Product B requires 3 hours
• We have 40 total machine hours
• Profit is 30 for A and $50 for B
• Objective: maximize profit

Modeling the Problem

Let:

• $x$ - number of units of Product A
• $y$ - number of units of Product B

Constraints:

Objective:

PuLP prints the optimal values:

• How many units of each product should be produced
• The maximum achievable profit
• Which constraints are binding (tight) vs non-binding

The results give actionable insights: "Produce more of the item with higher marginal profit until the machine constraint becomes binding".