Let's break down the problem to create a mathematical model:

Variables:

Let:

• $x$ = area in $m^2$ used for planting chili peppers (cabai)
• $y$ = area in $m^2$ used for planting tomatoes (tomat)

Constraints:

1. Total land area: $x + y \leq 10,000 \, m^2$

2. Fertilizer constraints:

   • Fertilizer A: $2x + 1y \leq 18,000 \, \text{kg}$ (2 kg/m² for chili and 1 kg/m² for tomatoes)

   • Fertilizer B: $1x + 2y \leq 16,000 \, \text{kg}$ (1 kg/m² for chili and 2 kg/m² for tomatoes)

Objective:

Maximize the use of available land without exceeding fertilizer limits.

Now, solving this linear programming problem requires finding the maximum area combination for $x$ and $y$ that adheres to these constraints.

Would you like a detailed step-by-step solution, or a numerical answer to the maximum land area that can be planted for each crop?

Related Questions:

1. What happens if the constraints for fertilizer change?
2. How would the model adjust if the maximum land area increases?
3. What if another type of plant with different fertilizer needs is introduced?
4. How does the maximum area change if fertilizer A or B has a higher total limit?
5. What if the cost of fertilizers A and B is introduced into the optimization?

Tip:

To solve optimization problems like this, using the Simplex Method or a graphing method can visually confirm the feasible region and the optimal solution.