Solution:

The given linear inequalities are:

2x + y > 18 ……(i)

x + y ≥ 12 ……(ii)

3x + 2y ≤ 34 ……(iii)

Graphical representation of the inequalities:

(i) 2x + y > 18

Let's plot the line 2x + y = 18 first.

When x = 0, y = 18

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

Joining these two points, we get the line 2x + y = 18.

As the inequality is greater than, the region above the line 2x + y = 18 is the feasible region.

(ii) x + y ≥ 12

Let's plot the line x + y = 12 next.

When x = 0, y = 12

When y = 0, x = 12

Joining these two points, we get the line x + y = 12.

As the inequality is greater than or equal to, the region above and on the line x + y = 12 is the feasible region.

(iii) 3x + 2y ≤ 34

Let's plot the line 3x + 2y = 34 next.

When x = 0, y = 17

When y = 0, x = 11.33

Joining these two points, we get the line 3x + 2y = 34.

As the inequality is less than or equal to, the region below and on the line 3x + 2y = 34 is the feasible region.

Common feasible region:

The feasible region for the system of linear inequalities is the region common to all the three regions obtained from individual inequalities.

The common region in the graph of linear inequalities 2x + y > 18, x + y ≥ 12 and 3x + 2y ≤ 34 is the region that is above the line 2x + y = 18 and on or above the line x + y = 12 and below or on the line 3x + 2y = 34.

Hence, the common feasible region is feasible and bounded.

Therefore, the correct option is (c) feasible and bounded.

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