Linear programming (linprog) in SciPy - Mini Project: Build & Apply

Linear Programming with scipy.linprog

📖 Scenario: You are managing a small factory that produces two products: chairs and tables. You want to maximize your profit while considering the limits on materials and labor hours.

🎯 Goal: Build a linear programming model using scipy.optimize.linprog to find the best number of chairs and tables to produce to maximize profit.

📋 What You'll Learn

Create variables for the number of chairs and tables

Set up the profit coefficients for each product

Define the constraints for materials and labor

Use scipy.optimize.linprog to solve the problem

Print the optimal number of chairs and tables to produce

💡 Why This Matters

🌍 Real World

Factories and businesses use linear programming to maximize profits or minimize costs while respecting resource limits.

💼 Career

Understanding linear programming is useful for roles in operations research, supply chain management, and data science.

1

Set up profit coefficients and variables

Create a list called profit_coeffs with values -20 and -30 representing the negative profit per chair and table respectively (negative because linprog minimizes).

SciPy

# Create the list profit_coeffs with values -20 and -30
# Your code here

Need a hint?

Remember, linprog minimizes, so use negative profits to maximize.

2

Define constraints for materials and labor

Create a list of lists called constraints_matrix with these rows: [1, 2] for wood usage and [3, 2] for labor hours. Also create a list called constraints_limits with values 100 and 90 representing the maximum wood and labor available.

SciPy

profit_coeffs = [-20, -30]
# Create constraints_matrix and constraints_limits as described
# Your code here

Need a hint?

Each row in constraints_matrix corresponds to a resource limit.

3

Use linprog to solve the optimization problem

Import linprog from scipy.optimize. Then create a variable called result by calling linprog with profit_coeffs as the objective, constraints_matrix as A_ub, and constraints_limits as b_ub. Use default bounds.

SciPy

profit_coeffs = [-20, -30]
constraints_matrix = [[1, 2], [3, 2]]
constraints_limits = [100, 90]
# Import linprog and solve the problem, store in result
# Your code here

Need a hint?

Use c= for objective coefficients, A_ub= and b_ub= for inequality constraints.

4

Print the optimal production quantities

Print the string Optimal chairs: followed by the first value in result.x and the string Optimal tables: followed by the second value in result.x. Use two separate print statements.

SciPy

from scipy.optimize import linprog

profit_coeffs = [-20, -30]
constraints_matrix = [[1, 2], [3, 2]]
constraints_limits = [100, 90]

result = linprog(c=profit_coeffs, A_ub=constraints_matrix, b_ub=constraints_limits)
# Print optimal chairs and tables
# Your code here

Need a hint?

Access the solution with result.x and print the values.