Question

Solve the following model using linear programming and determine the values of the decision variables and objective function. Then, round the decision variables values down to the nearest integer and determine the value of the decision variables and objective function, this is an approximate answer to solving the model using integer programming. Observe if the rounding provides a "feasible" solution, all constraints are satisfied. Finally, solve the model using integer programming and determine the values of the decision variables and the objective function using integer constraints. Observe the differences in the answers using the three methods. Maximize Z = 2x1 + 6x2 + 3x3 subject to 1x1 + 1x2 + 1x3 ≤ 7 -1x1 + 1x2 + -1x3 ≤ -6 -1x1 + 1x2 + -2x3 ≤ -3 x1, x2, x3 ≥ 0

LP Method

x1 =

x2 =

x3 =

Z* =

Round Down Method

x1 =

x2 =

x3 =

Z* =

IP Method

x1 =

x2 =

x3 =

Z* =

(Show excel formulas)

Answer 1

Excel model for LP method:

Solver inputs:

Solution:

So,

x1 = 0
x2 = 0.5
x3 = 6.5
Z* = 22.5

------------------------------------------

Round-down method:

x1 = 0
x2 = 0
x3 = 6
Z* = 2*0+6*0+3*6 = 18

------------------------------------------

IP method:

Add the following additional constraint in the Solver:

Solution:

x1 = 0
x2 = 0
x3 = 7
Z* = 21