Blending / Recipe - Handbook

Type: LP (Linear Programming)

This handbook explains the Blending / Recipe sample problem in the LP Black Box platform.

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The Problem

Scenario

Create a 100-unit product blend using three ingredient grades to meet quality standards at minimum cost.

Ingredient	Cost ($)	Quality Score
Grade A	50	95
Grade B	30	80
Grade C	15	60

Your Goal

Minimize total cost while meeting quality requirements.

The Constraints

1. Total Amount: Must use exactly 100 units

   Formula: gradeA + gradeB + gradeC = 100

2. Quality: Average quality must be at least 75

   Formula: 95×gradeA + 80×gradeB + 60×gradeC ≥ 7500

   (Note: 75 × 100 = 7500)

3. Max Grade A: Cannot use more than 40 units of Grade A

   Formula: gradeA ≤ 40

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How to Use

Step 1: Load the Sample

Select Blending / Recipe from the dropdown.

Step 2: Solve

The solver finds the optimal mix that meets quality standards at lowest cost.

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Try It Yourself

• Increase quality requirement to 80
• Remove the Grade A limit and see the cost difference

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This is a classic blending problem used in food, fuel, and manufacturing.