Question 3. Consider the following LP model formulated to find the critical path of a project network. x:= the time that the event of node i occurs, i = 1,2,3,4,5,6,7. dj = the duration of activity j j = A,B,C,D,E,F,G,H. Min z=X7-X1 X2 - X ds (1) X3 - XI dA (2) X3 - X20 (3) X-X12dc (4) X-X220 (5) Xs - X: de (6) Xs - X; do (7) X6-X620 (8) X7-X df (9) X7-Xs du (10) X7-Xs> da (11) x20 for i=1,2,3,4,5,6,7 a. Draw the activity-on-arc representation of the project network. (10 points) b. In the optimal solution of the above LP, the shadow prices of constraints (1) to (11) are as given. Constraint (1) (2) (3) (4) (5) 6 (7) (8) (9) (10) (11) Shadow Price 10 1 0 0 0 1 0 0 0 1 i Identify the critical path and show it on the network. (4 points) ii. What happens to the project completion time if the duration of activity G increases by 3 days? (3 points) iii. What happens to the project completion time if the duration of activity H increases by 3 days? (3 points)