6. Consider the following linear program: s.t. Max Z = 2x1 + x2 + 3x3 X1 + 4x2 + 4x3 s 20 4x2 + 4x2 + x3 = 20 x 20 for j = 1,2,3 The solution to this problem using SOLVER is given below: X1 2 4 X2 1 0 X3 3 4 Obj Fet Dec Var CST 1 CST 2 20 1 4 4 1 20 20 20 Variable Cells Cell Name $B$3 $C$3 SD$3 Dec Var x1 Dec Var x2 Dec Var x3 Final Value 4 0 4 Reduced Cost 0 -3 0 Objective Coefficient 2 1 3 Allowable Allowable Increase Decrease 10 1.25 3 1E+30 S 2.5 Constraints Cell Name $D$5 SD$6 Final Value 20 20 Shadow Price 0.666666667 0.333333333 Constraint Allowable R.H. Side Increase 20 60 20 60 Allowable Decrease 15 15 Constrainti Constraint2 Use the SOLVER output to answer the following questions: a) What are the optimal solution and the optimal value? b) For what values of does the current solution remain optimal? c) If = 11, what is the optimal value? d) For what values of Cz is the current solution optimal? e) If one had 65 units of resource 2 (bz), then what would be the optimal value? f) What does the (-3) in the reduced cost column mean? g) What is the dual of this LP problem and what is its optimal solution and value