`x + 2y le 10, x + y ge 1, x-y le 0, x ge 0, yge 0`

Explanation

To solve the given inequalities graphically, we will follow these steps:

### Step 1: Convert Inequalities to Equations
We start by converting each inequality into an equation to find the boundary lines.

1. **First Inequality:** \( x + 2y \leq 10 \) becomes \( x + 2y = 10 \).
2. **Second Inequality:** \( x + y \geq 1 \) becomes \( x + y = 1 \).
3. **Third Inequality:** \( x - y \leq 0 \) becomes \( x - y = 0 \).
4. **Fourth Inequality:** \( x \geq 0 \).
5. **Fifth Inequality:** \( y \geq 0 \).

### Step 2: Find Intercepts for Each Line
Next, we find the intercepts for each equation to plot them.

1. **For \( x + 2y = 10 \):**
- Let \( x = 0 \): \( 2y = 10 \) → \( y = 5 \) (Point: \( (0, 5) \))
- Let \( y = 0 \): \( x = 10 \) (Point: \( (10, 0) \))

2. **For \( x + y = 1 \):**
- Let \( x = 0 \): \( y = 1 \) (Point: \( (0, 1) \))
- Let \( y = 0 \): \( x = 1 \) (Point: \( (1, 0) \))

3. **For \( x - y = 0 \):**
- Let \( x = 0 \): \( y = 0 \) (Point: \( (0, 0) \))
- Let \( y = 0 \): \( x = 0 \) (Point: \( (2, 2) \))

### Step 3: Plot the Lines
Now we plot the lines based on the points obtained:

1. **Line for \( x + 2y = 10 \)**: Connect points \( (0, 5) \) and \( (10, 0) \).
2. **Line for \( x + y = 1 \)**: Connect points \( (0, 1) \) and \( (1, 0) \).
3. **Line for \( x - y = 0 \)**: Connect points \( (0, 0) \) and \( (2, 2) \).

### Step 4: Determine the Shading Region
Next, we determine which side of each line to shade based on the inequality:

1. **For \( x + 2y \leq 10 \)**: Test point \( (0, 0) \):
- \( 0 + 2(0) \leq 10 \) → True, so shade below the line.

2. **For \( x + y \geq 1 \)**: Test point \( (0, 0) \):
- \( 0 + 0 \geq 1 \) → False, so shade above the line.

3. **For \( x - y \leq 0 \)**: Test point \( (10, 0) \):
- \( 10 - 0 \leq 0 \) → False, so shade below the line.

4. **For \( x \geq 0 \)** and **\( y \geq 0 \)**: Shade in the first quadrant.

### Step 5: Identify the Feasible Region
The feasible region is where all shaded areas overlap. This region will be bounded by the lines and will be in the first quadrant.

### Final Graph
Draw the axes, plot the lines, and shade the feasible region based on the above conditions.

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