a. Formulate the dual of the following linear programming model: [8] Max Z = 45X: +28X2 - 32X3 + 16X Such that: 14X: +25X2 - 20X3 = 24 18X, - 10X2 + 30X3 + 22X2 15 26X: + 34X2 - 12X4 25 X1, X3, X4 20 X2 - unrestricted b. A plant installation project involves ten (10) activities. The activity times and the precedence relationships are shown in Table 4. Activity Predecessor Table 4 Activity a b d Activity Duration (weeks) 5 7 b b d e f 8 6 9 8 7 a, c a 8 h i a, c e, f 6 10 5 i. ii. iii. Construct a CPM network representing the installation project. Determine the critical path and the minimum duration of the project. Determine the free and total slack of all non-critical activities