PuLP for linear optimization

A farmer faces a diet problem for their cattle. The vet's recommendation is that each animal is fed at least 7 pounds of a mix of corn and soybean with at least 17% protein and 2% fat. Below are the relevant nutritional elements:

Food type	Cost ($/lb)	Protein (%)	Fat (%)
corn	0.11	10	2.5
soybean	0.28	40	1

You will use this information to minimize costs subject to nutritional constraints.

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Introduction to Optimization in Python

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Introduction to Optimization in Python

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This chapter introduces optimization, its core components, and its wide applications across industries and domains. It presents a quick, exhaustive search method for solving an optimization problem. It provides a mathematical primer for the concepts required for this course.

Exercise 1: Introduction to mathematical optimization Exercise 2: Understanding mathematical optimization Exercise 3: Applying an objective function Exercise 4: Exhaustive search method Exercise 5: Univariate optimization Exercise 6: Finding the derivative Exercise 7: Find the second derivative Exercise 8: Multivariate optimization Exercise 9: Partial derivatives with SymPy Exercise 10: Limitations of differentiation

This chapter covers solving unconstrained and constrained optimization problems with differential calculus and SymPy, identifying potential pitfalls. SciPy is also introduced to solve unconstrained optimization problems, in single and multiple dimensions, numerically, with a few lines of code. The chapter goes on to solve linear programming in SciPy and PuLP.

Exercise 1: Unconstrained optimization Exercise 2: Finding the maxima Exercise 3: Multivariate optimization Exercise 4: Bound-constrained optimization Exercise 5: Working with Bounds Exercise 6: Handling hard inequalities Exercise 7: Linear programming Exercise 8: What is linear programming?Exercise 9: PuLP for linear optimization

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Exercise 10: Handling multiple elements

This chapter introduces convex-constrained optimization problems with different constraints and looks at mixed integer linear programming problems, essentially linear programming problems where at least one variable is an integer.

Exercise 1: Convex constrained-optimization Exercise 2: Interpreting indifference curves Exercise 3: Visualize the indifference curve Exercise 4: Utility maximization Exercise 5: Convex-constrained optimization with inequality constraints Exercise 6: Interior or corner?Exercise 7: Linear constrained biscuits Exercise 8: Nonlinear constrained biscuits Exercise 9: Mixed integer linear programming (MILP)Exercise 10: Adjusting MILP Exercise 11: Understanding integrality

This chapter covers finding the global optimum when multiple good solutions exist. We will conduct sensitivity analysis and learn linearization techniques that reduce non-linear problems to easily solvable ones with SciPy or PuLP. In terms of applications, we will solve an HR allocation with training costs problem and capital budgeting with dependent projects.

Exercise 1: Transforming non-linear problems Exercise 2: Solving the capital budgeting problem Exercise 3: Allocating resources Exercise 4: Global optimization in SciPy Exercise 5: Find the global optimum Exercise 6: Using callback Exercise 7: Sensitivity analysis in PuLP Exercise 8: Slack and shadow price Exercise 9: Shadow prices with juice Exercise 10: The diet problem revisited Exercise 11: Congratulations!