Consider the inequalities `x_1+x_2 le 3,2x_1+5x_2ge 10x_1,x_2 ge 0` then feasible region is

Options

A. (2,2)
B. (1,2)
C. (2,1)
D. (4,2)

Explanation

To find the feasible region defined by the inequalities \( x_1 + x_2 \leq 3 \), \( 2x_1 + 5x_2 \geq 10 \), and \( x_1, x_2 \geq 0 \), we will follow these steps:

### Step 1: Graph the first inequality \( x_1 + x_2 \leq 3 \)

1. **Find the intercepts**:
- Set \( x_1 = 0 \): \( x_2 = 3 \) (point \( (0, 3) \))
- Set \( x_2 = 0 \): \( x_1 = 3 \) (point \( (3, 0) \))

2. **Draw the line**:
- Plot the points \( (0, 3) \) and \( (3, 0) \) on the graph.
- Draw a line through these points. Since the inequality is \( \leq \), shade the area below the line.