Diet Optimization - Handbook

Type: LP (Linear Programming)

This handbook explains the Diet Optimization sample problem in the LP Black Box platform.

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The Problem

Scenario

Plan a daily menu using four foods to meet nutritional requirements at minimum cost.

Food	Cost ($)	Calories	Protein (g)	Iron (mg)
Bread	2	50	2	1
Milk	3	100	8	0.1
Meat	8	200	25	3
Vegetables	4	30	3	2

Your Goal

Minimize total food cost while meeting daily nutritional requirements.

The Constraints

1. Calories: At least 2000 calories

   Formula: 50×bread + 100×milk + 200×meat + 30×veg ≥ 2000

2. Protein: At least 50g

   Formula: 2×bread + 8×milk + 25×meat + 3×veg ≥ 50

3. Iron: At least 15mg

   Formula: 1×bread + 0.1×milk + 3×meat + 2×veg ≥ 15

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How to Use

Step 1: Load the Sample

Select Diet Optimization from the dropdown.

Step 2: Solve

The solver finds the cheapest combination that meets all nutritional needs.

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Try It Yourself

• Add a maximum calorie constraint (≤ 2500)
• Add vitamin requirement with new foods

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This classic LP problem demonstrates how to meet multiple requirements at minimum cost.