The problem describes a situation where a farmer wants to plant two types of crops: chili peppers (cabai) and tomatoes (tomat). The farmer has 10,000 m² of land and specific amounts of fertilizers A and B for each type of plant.

Problem Breakdown:

• Land area: 10,000 m² total
• Fertilizer requirements for chili (cabai):
  • Fertilizer A: 2 kg/m²
  • Fertilizer B: 1 kg/m²
• Fertilizer requirements for tomatoes (tomat):
  • Fertilizer A: 1 kg/m²
  • Fertilizer B: 2 kg/m²
• Total fertilizer available:
  • Fertilizer A: 18,000 kg
  • Fertilizer B: 16,000 kg

1. Mathematical Model:

Let:

• $x$ = the area (in m²) planted with chili
• $y$ = the area (in m²) planted with tomatoes

The total land available is 10,000 m², so: $x + y \leq 10,000$

For the fertilizer constraints:

• Fertilizer A: The total fertilizer A required is given by $2x + y$, and the available amount is 18,000 kg. Thus: $2x + y \leq 18,000$
• Fertilizer B: The total fertilizer B required is given by $x + 2y$, and the available amount is 16,000 kg. Thus: $x + 2y \leq 16,000$

2. Maximum Area to Plant:

We need to solve these inequalities to find the maximum area of land that can be planted with chili and tomatoes, using all available fertilizer.

The system of inequalities is: $x + y \leq 10,000$ $2x + y \leq 18,000$ $x + 2y \leq 16,000$

We can solve this system graphically or using linear programming to maximize the land used, subject to these constraints. Let me know if you'd like me to solve this step-by-step!

Do you have any questions or want more details?

Related Questions:

1. How would the solution change if the available fertilizer B was reduced to 15,000 kg?
2. What happens if the farmer decides to prioritize planting tomatoes over chili?
3. How much fertilizer would be required if the entire 10,000 m² was used to plant only chili?
4. How much land would be left unused if the farmer used all available fertilizers but didn’t reach the 10,000 m²?
5. How could the farmer adjust the proportions of chili and tomato planting to use the least amount of fertilizer?

Tip:

When modeling real-world problems, identifying the correct constraints and translating them into mathematical inequalities is key to finding optimal solutions.