Solve the linear programming problem:
MaxZ=3x₁+2x₂ Subjected to
4x₁+3x₂<=12
4x₁+x₂<=8
4x₁-x₂<=8
x₂>=0
a) Graph the feasible region.
b) Calculate the maximum value of Z.
c) Identify the optimal solution.
d) Determine the shadow prices of constraints.