4. (20 points) Consider the maximization problem given below. The following tables are the solution of the problem and sensitivity analysis. Decision variables x2 3.47222 1.66667 x1 175 60 = 707.639 Max zu s.t. 12 1 0 5 = 1 = 15 = 50 50 10 25 Objective Cell (Max) Cell Name Original Value Final Value $G$16 = 7100 707.6388889 Variable Cells Cell Name Original Value Final Value Integer $D$14 x1 20 3.472222222 Contin $E$14 x2 60 1.666666667 Contin Constraints Cell Name $G$18= $G$19 = $G$20 = Cell Value Formula Status Slack 50 $G$18=$i$20 Binding 0 Variable Cells Cell Name $D$14 x1 $E$14 x2 Final Value 3.47222222 1.66666667 Reduced Objective Allowable Cost Coefficient Increase 0 175 1E+30 0 60 12.9166667 Allowable Decrease 31 1E30 Constraints Cell Name $G$18= $G$19 = $G$20 = Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 50 14.58333333 50 58.3333333 41.6666667 5.13888889 0 10 1E+30 4.86111111 25 -0.86111111 25 125 25 Answer the following short questions according to the problem above. For full credit, you must show all your calculations. (a) (3 points) If the right-hand side value of the first constraint increases from 50 to 52, the objective function value increases to 709.639. TRUE or FALSE? (b) (3 points) Explain your answer above. Why? (e) (3 points) If the right-hand side value of the second constraint increases from 10 to 20, the new objective function value would be 717.393. TRUE or FALSE? (d) (3 points) If the right-hand side value of the third constraint increases from 25 to 155, the new objective function value decreases by 86.1111. TRUE or FALSE? (e) (3 points) If the objective coefficient of the first decision variable (11) decreases from 175 to 165, be the new objective function value decreases by 34.722. TRUE or FALSE? (f) (5 points) How do we use sensitivity analysis in real life problems? What kind of man- agerial decisions can we make? And, how