Math Problem Statement

Seorang petani ingin menanam dua jenis tanaman, yaitu cabai dan tomat. Ia memiliki lahan seluas 10.000 m². Untuk menanam cabai, dibutuhkan pupuk A sebanyak 2 kg/m² dan pupuk B sebanyak 1 kg/m². Sedangkan untuk menanam tomat, dibutuhkan pupuk A sebanyak 1 kg/m² dan pupuk B sebanyak 2 kg/m². Petani tersebut memiliki persediaan pupuk A sebanyak 18.000 kg dan pupuk B sebanyak 16.000 kg. Buatlah model matematika dari permasalahan tersebut! Berapa luas lahan maksimum yang dapat ditanami cabai dan tomat agar pupuk yang tersedia habis?

Solution

Let's break down the problem and set up the mathematical model based on the information provided:

Variables:

Let:

  • xx be the area (in m2m^2) used to plant chili peppers (cabai).
  • yy be the area (in m2m^2) used to plant tomatoes (tomat).

Constraints:

  1. Land constraint: The total land available is 10,000 m², so: x+y≤10,000x + y \leq 10,000

  2. **

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Math Problem Analysis

Mathematical Concepts

Linear Programming
System of Inequalities

Formulas

x + y ≤ 10,000 (land constraint)
2x + 1y ≤ 18,000 (fertilizer A constraint)
1x + 2y ≤ 16,000 (fertilizer B constraint)

Theorems

Optimization with Linear Constraints

Suitable Grade Level

High School or early college

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