Question

Question 5 options:

Consider the following integer linear programming problem:

Max Z =       3x + 2y

Subject to:    3x + 5y ? 30

4x + 2y ? 28

                    x ? 8

                    x , y ? 0 and integer

The solution to the linear programming formulation is: x = 5.714, y = 2.571.

What is the optimal solution to the integer linear programming problem?

State the optimal values of decision variables and the value of the objective function.

Answer 1

answer...
Here as we are given the optimal solution as: x = 5.714 and y = 2.571
Here we are given the objective function as: Max: 3X + 2Y, therfore we just need the max values of X and Y here.
First we check here whether X = 6, Y = 3 to check whether they satisfy the constraints.
3X + 5Y = 3*6 + 5*3 = 33 not less than 30, therefore now we check
X = 6, Y = 2, we get:
3X + 5Y = 3*6 + 5*2 = 28 < 30
4X + 2Y = 24 + 4 = 28 <= 28
Therefore, we get the solution here as: X = 6 and Y = 2
Therefore we get here that:
X = 6 and Y = 2
value of obj function = 3X + 2Y = 22