Consider the linear program

Maximize z = x1,

subject to:

x1 + x2 2,

x1 + x2 8,

x1 + x2 4,

x1 0, x2 0

a) State the above in canonical form.

b) Solve by the simplex method.

c) Solve geometrically and also trace the simplex procedure steps graphically.

d) Suppose that the objective function is changed to z = x1 + cx2. Graphically determine the values of c for which the solution found in parts (b) and (c) remains optimal.

e) Graphically determine the shadow price corresponding to the third constraint