Solve the following model using linear programming (allow for continuous values) 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 = 1x1 + 5x2 + 4x3 subject to 1x1 + 1x2 + 1x3 6 -2x1 + 1x2 + -1x3 -7 -1x1 + -1x2 + 1x3 1 x1, x2, x3 0 LP Method x1 = x2 = x3 = Z* = Round Down Method x1 = x2 = x3 = Z* = IP Method x1 = x2 = x3= Z*=