Solution:

To find the common region in the graph of linear inequalities, we need to follow these steps:

Step 1: Graph each inequality separately.

Step 2: Identify the region that satisfies all the inequalities.

Step 3: Shade the common region.

Graph each inequality separately:

To graph the inequalities, we can start by finding the intercepts:

2x + y ≥ 18

When x = 0, y = 18

When y = 0, 2x = 18, x = 9

So the intercepts are (0, 18) and (9, 0)

To graph the inequality, we can plot these intercepts and draw a line through them. Then we can shade the region above the line, since it is the region that satisfies the inequality.

x*y ≥ 12

When x = 0, y can be any value

When y = 0, x = undefined

So the intercepts are (0, any value) and (undefined, 0)

To graph the inequality, we can plot these intercepts and draw a line through them. Then we can shade the region above and to the right of the line, since it is the region that satisfies the inequality.

3x + 2y ≤ 34

When x = 0, y = 17

When y = 0, 3x = 34, x = 11.3333

So the intercepts are (0, 17) and (11.3333, 0)

To graph the inequality, we can plot these intercepts and draw a line through them. Then we can shade the region below the line, since it is the region that satisfies the inequality.

Identify the region that satisfies all the inequalities:

To identify the region that satisfies all the inequalities, we need to look for the overlapping regions of the shaded areas. We can see that the common region is the region that is shaded above and to the right of the line x*y = 12 and below the line 3x + 2y = 34.

Shade the common region:

To shade the common region, we can use a darker shade to fill in the area that satisfies all the inequalities.

Final Answer:

The common region in the graph of linear inequalities 2x+y≥18, x*y≥12 and 3x+2y≤34 is the shaded area above and to the right of the line x*y = 12 and below the line 3x + 2y = 34.