Explanation:

- The objective function to maximize is z = 4x + 2y.

- Constraints are:

- \(2x + 3y \leq 28\)

- \(x + y \leq 10\)

- \(x, y \geq 0\)

- Find intersections that's feasible:

- Intersection of \(2x + 3y = 28\) and \(x + y = 10\) gives a point.

- Check vertices: (0, 0), intersection points, and boundaries.

- Calculate z at each feasible vertex:

- Option 1: 36 – Try feasible points; compute to match.

- Option 2: 40 – Check if it aligns with results.

- Option 3: \( \frac{100}{3} \) ˜ 33.33 – Consider alternative calculations.

- Option 4: 32 – Evaluate if plausible.

- Maximize z at feasible points.

- The correct answer is Option 2: 40.