A farmer wants to maximize profit from selling onions and greens. Onions yield 500,000 profit/ton and greens yield 300,000 profit/ton. The farmer has 10 hectares of land (onions: 1 ha/ton, greens: 2 h

Let $x$ be the number of tons of onions.
Let $y$ be the number of tons of greens.

The farmer wants to maximize profit.
Profit from onions: Ugx. 500,000 per ton.
Profit from greens: Ugx. 300,000 per ton.
The objective function to maximize is:

• Land Constraint: The farmer has "almost ten hectares" of land. Onions need 1 hectare per ton, and greens need 2 hectares per ton. $$1x + 2y \le 10$$
• Labor Constraint: The farmer intends to spend "not more than 120 hours per week" on labor. Onions require 2 hours per ton, and greens require 3 hours per ton. $$2x + 3y \le 120$$
• Non-negativity Constraints: The number of tons of crops cannot be negative. $$x \ge 0$$ $$y \ge 0$$

The required inequalities are:

Task (b):

To graph the inequalities, we consider their boundary lines:

1. For $x + 2y = 10$: If $x=0$, $2y=10 \Rightarrow y=5$. Point: $(0, 5)$. If $y=