Consider the following Linear Program:
max z = x1 + 2x2
s/t x1 + 3x2 <= 8
x1 + x2 <= 4
x1, x2 >= 0
a) Solve the above LP graphically. Label each constraint, shade the feasible region, draw the isovalue line, indicate the direction of improvement for the isovalue line, and use the binding constraints to determine the optimal solution (or clearly explain why no optimal solution exists).
b) What is the allowable range for the optimal solution to stay optimal for the coefficient of x2 in the objective function assuming that x1 remains fixed?