Graph the feasible region subject to the following constraints.6𝑥 − 8𝑦 ≤ 12 ; 3𝑥 + 4𝑦 ≥ 6 ; 𝑥 ≥ 0 ; 𝑦 ≥ 0

To graph the feasible region, we need to plot the boundary lines of the given constraints and shade the region that satisfies all the constraints.

1. Start by graphing the first constraint: 6𝑥 − 8𝑦 ≤ 12. To do this, we can rewrite the inequality as an equation and plot the corresponding line.

   6𝑥 − 8𝑦 = 12 -8𝑦 = -6𝑥 + 12 𝑦 = (3/4)𝑥 - 3/2

   Plot the line 𝑦 = (3/4)𝑥 - 3/2 on the coordinate plane.

2. Next, graph the second constraint: 3𝑥 + 4𝑦 ≥ 6. Again, rewrite the inequality as an equation and plot the line.

   3𝑥 + 4𝑦 = 6 𝑦 = (-3/4)𝑥 + 3/2

   Plot the line 𝑦 = (-3/4)𝑥 + 3/2 on the coordinate plane.

3. Now, consider the constraints 𝑥 ≥ 0 and 𝑦 ≥ 0. These constraints simply mean that 𝑥 and 𝑦 must be non-negative, so we need to shade the region in the first quadrant of the coordinate plane.

4. Finally, identify the region where all the shaded areas overlap. This region represents the feasible region that satisfies all the given constraints.

The graph of the feasible region should show the shaded area in the first quadrant of the coordinate plane, bounded by the lines 𝑦 = (3/4)𝑥 - 3/2 and 𝑦 = (-3/4)𝑥 + 3/2.