# Convex Optimisation Example: Nutritionist

This example gives a problem in the form of a real-world description, and asks for a mathematical formulation of the optimisation problem. In this video, I only do the conversion step, and don’t solve the optimisation problem. The question is listed below, but I encourage you to mark off each piece of information as it is used in your lecture notes (the example appears on page 64).

The inequalities in the constraints may be simplified by dividing everything by 30, but I didn’t do this. It would make calculations a little easier, if you go on to solve this problem yourself.

==== Statement of problem ====

A nutritionist is planning a menu that includes foods A and B as its main staples. Suppose that each gram of food A contains 60 units of protein, 30 units of iron, and 30 units of thiamine; each gram of food B contains 30 units of protein, 30 units of iron, and 90 units of thiamine. Suppose that each gram of A costs 2 cents, while each gram of B costs 3 cents. The nutritionist wants the meal to provide at least 360 units of protein, at least 270 units of iron, and at least 450 units of thiamine. How many grams of each of the foods should be used to minimise the cost of the meal?