For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are

$3x+4y ≤24,x + 2y ≥ 10,x ≥0,y ≥0$

The correct answer is Option (4) → $3x+4y ≤24,x + 2y ≥ 10,x ≥0,y ≥0$

Given: The shaded region is bounded by two lines and lies in the first quadrant.

The lines are:

1. $x + 2y = 10$

2. $3x + 4y = 24$

The feasible region lies below both lines and in the first quadrant (i.e., $x \geq 0,\ y \geq 0$).

So, the inequalities are:

$x + 2y \geq 10$

$3x + 4y \leq 24$

$x \geq 0$

$y \geq 0$