*Instead of nutritional values, you will have profits and other types of business yields, and in place of price/serving, you may have project costs in thousands of dollars.*As a manager, your job will be to choose the projects, that give maximum return on investment without exceeding a total budget of funding the project.

*Instead of nutritional values, you will have profits and other types of business yields, and in place of price/serving, you may have project costs in thousands of dollars.*

Linear and (mixed) integer programming are techniques to solve problems which can be formulated within the framework of discrete optimization.

Knowledge of such optimization techniques is extremely useful for data scientists and machine learning (ML) practitioners as discrete and continuous optimization lie at the heart of modern ML and AI systems as well as data-driven business analytics processes.

The following table shows, in detail, the complete nutritional value for each food item, and their maximum/minimum daily intake.

The discrete optimization problem is simple: Minimize the cost of the lunch given these constraints (on total calories but also on each of the nutritional component e.g.

In fact, integer programming is a harder computational problem than linear programming.

Integer variables make an optimization problem non-convex, and therefore far more difficult to solve.cholesterol, vitamin A, calcium, multiplied by constant coefficients and the resulting terms are bounded by constant limits and that’s what makes this problem solvable by an LP technique.You can imagine that this kind of problem may pop up in business strategy extremely frequently.The full solution contains all the variables including the ones with zero weights.But to us, only those variables are interesting which have non-zero coefficients i.e. So, we can scan through the problem variables and print out only if the variable quantity is positive. cost of the diet in this case, As we can see that the optimal result came back with a set of fractional numbers of servings for the food items.For the diet problem, the objective function is the total cost which we are trying to minimize.The inequality constraints are given by the minimum and maximum bounds on each of the nutritional components.It also integrates nicely with a range of open source and commercial LP solvers.You can install it using pip (and also some additional solvers)We have done the hard part.There are many libraries in the Python ecosystem for this kind of optimization problems.Pu LP is an open-source linear programming (LP) package which largely uses Python syntax and comes packaged with many industry-standard solvers.

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