Oppiskele Solving LPs in Python with pulp | Foundations of Optimization for Analytics

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:

2x + 3y \le 40

Objective:

\max(30x + 50y)


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from pulp import LpProblem, LpVariable, LpMaximize, value

# Create optimization model
model = LpProblem("Production_Optimization", LpMaximize)

# Decision variables
x = LpVariable("Product_A", lowBound=0)
y = LpVariable("Product_B", lowBound=0)

# Objective function
model += 30 * x + 50 * y

# Constraint: machine hours
model += 2 * x + 3 * y <= 40

# Solve
model.solve()

print("Optimal Production Plan:")
print("Product A:", value(x))
print("Product B:", value(y))
print("Max Profit:", value(model.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".

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Suggested prompts:

Can you explain what a binding constraint means in this context?

How would I add more constraints, like material limits, to the model?

What if I want to minimize costs instead of maximizing profit?

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