How to Formulate Linear Programming Problems in Applied Mathematics: CBSE Class 12 Fertilizer Cost Example

LPP Cost Minimization CBSE 12 | Math Model Solved Fast

When it comes to Applied Mathematics in Class 12, one of the most practical and widely used concepts is Linear Programming. It combines logic, algebra, and real-world decision-making. This blog post dives deep into one of the most essential board-level problems where a farmer must decide how to mix two types of fertilizers to minimize his cost while fulfilling soil requirements. If you’re preparing for your board exams, competitive tests, or just want a better understanding of how math is used in agriculture and economics, this is for you.

✅ Watch the full video below to follow along with the step-by-step solution and see how real exam questions are approached.

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Understanding the Problem

In this classic board exam question from the CBSE Class 12 Applied Mathematics curriculum, a farmer needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for his crop. There are two types of fertilizers available:

• Fertilizer F₁ contains 10% nitrogen and 6% phosphoric acid and costs Rs.6 per kg.

• Fertilizer F₂ contains 5% nitrogen and 10% phosphoric acid and costs Rs.5 per kg.

The objective is to minimize the total cost while meeting the nutrient requirements of the soil.

To solve this problem, we must formulate it as a linear programming problem (LPP). This is exactly the type of modeling question that appears frequently in the CBSE Class 12 Applied Mathematics board paper, particularly in the 2024 and 2025 editions. It also aligns with the expectations from ISC Applied Maths, IGCSE Extended Maths, IB Diploma HL and SL, Edexcel A Level Maths, and even entrance-oriented mathematics found in economics and business-related exams.

Minimize:
Z = 6x + 5y

Subject to:
2x + y ≥ 280
3x + 5y ≥ 700
x ≥ 0, y ≥ 0

Why This Problem Matters

This problem is not just academic. It is a direct representation of how mathematics supports cost-effective decision-making in industries like farming, manufacturing, and logistics. When framed properly, such problems lead to linear optimization models, which are used globally in business and operations research. Understanding how to formulate these problems accurately is essential for students aiming to work in economics, agriculture planning, data science, supply chain, and more