Consider the following LP model. minz=7x1 +2x2 s.t. x2 =8 (cons2) 3x1+4x2 =9 (cons4) x1 >=0 x2>=0

Consider the following LP model.

minz=7x1 +2x2 

s.t.
x2 <= 4.             (cons1)
2x1+x2 >=8       (cons2)

 3x1+4x2 <=24  (cons3)

 x1 +3x2 >=9     (cons4)

x1 >=0

x2>=0
a) Solve the above model graphically. Identify the feasible region on the graph provided below and find the optimal solution.

b) What is the slack amount for constraint (3) in the optimal solution?

c) Find the allowable increase and decrease for c2 (the objective function coefficient of x2) for which the current solution remains optimal (given c1=7).

d) What is the value of c1 that would result in alternative optimal solutions which are on the line segment [AB], given c2=2?

e) Find the shadow prices of constraints (2) and (3). Interpret.

f) What would the optimal objective function value be if the right hand side value of constraint (1) is decreased from 4 to 5/2?