Question

consider the following linear programming problem:

maximize \\(z = 1800x + 1000y\\) (profit in \\$)

subject to
\\3x + 2y \le 18\\
\\x + 2y \le 10\\
\\y \le 4\\
\\x, y \ge 0\\

a. select the correct feasible region.

Explanation:

Step1: Identify boundary lines

Find boundary lines from the inequalities.

$$
LATEXBLOCK0
$$

Step2: Find line intersections

Determine intersection points of the boundary lines.

$$
LATEXBLOCK1
$$

Step3: Determine corner points

Find all vertices of the feasible region.

$$ (0, 0), \quad (6, 0), \quad (4, 3), \quad (2, 4), \quad (0, 4) $$

Answer:

The feasible region is bounded by the corner points \((0, 0)\), \((6, 0)\), \((4, 3)\), \((2, 4)\), and \((0, 4)\).