[solved]-Consider The Following Optimization Problem Max Z X1 2×2 X3 X4 Subject To X1 X2 X3 2×4 15 X1 3 X2 3×3 5 X4 15 X1 X2 X3 X4 0 And Integers Which Of The Following Statements About The Problem A 63925

Consider the following optimization problem:max z = x1 + 2×2 + x3 + x4subject to: x1 + x2 + x3 + 2×4 <= 15×1> = 3×2 + 3×3 <= 5×4> = 1.5×1, x2, x3, x4> = 0 and integersWhich of the following statements about the problem arecorrect:1) The linear relaxation of the problem offers an upper limit(estimate of the maximum) for the optimal solution of theproblem.2) The solution X = (3 0 0 2) T is an infeasible solution to theproblem (T is the vector transpose)3) The most suitable method to obtain an optimal solution to theproblem consists of an explicit enumeration method (totalenumeration of the solutions and choice of the optimalsolution).4) The problem is a pure optimization problem.5) A method that always obtains an optimal solution to thisproblem is the rounding strategy, that is, the linear relaxationproblem is solved and the solution is rounded.6) If you take two feasible solutions to the problem andconnect, the segment will be within the feasible region of thisproblem (that is, if you take W and Z two whole solutions, whendoing the convex combination, all points T = aW + (1- a) Z, 0 <=a <= 1 are in the set of feasible solutions to the problem.

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