Consider the following IP problem.

Maximize z= 3x₁+ 2x₂,

subject to
Constraint 1:	2x1+ 3x2? 40,
Constraint 2:	3x1+x2? 30,
Constraint 3:	x1, x2? 0,
Constraint 4:	x1,x2= non-negative integer,

wherex₁andx₂represent the decision variables. Solve this IP problem and answer the following questions.

1. What are the values ofx₁andx₂at the optimal solution? What is the maximum value ofz?

Value of x1 at the optimal solution _____________

Value of x2 at the optimal solution _____________

Maximum value of z _____________

1. If the objective function coefficients change toz= 4x₁+ 3x₂, what are the values ofx₁andx₂at the optimal solution? What is the maximum value ofz?

Value of x1 at the optimal solution _____________

Value of x2 at the optimal solution _____________

Maximum value of z _____________

1. Using the original objective function coefficients, if the first constraint changes to2x₁+ 3x₂??47, what are the values ofx₁andx₂at the optimal solution? What is the maximum value ofz?

Value of x1 at the optimal solution _____________

Value of x2 at the optimal solution _____________

Maximum value of z _____________

Z= 31 + 22(2 maximum wave of z = 270- 38.57 7 value of X, at optimal solution = 50/7 = 7-14 value of 2 2 at optional Solution = 160/7 = 2.57 2 . ) Z= 4x1+2x2 and constraint not changed so, maximum value of z = 380- 54.28 value of x , at optimal Salution = 50/7 =7.14 value of 2 2 at optimal solution = 60/7 = 0.57 3 . ) Z = 32, +2x2 , but constring change first constraint changes to 2x2+3x2