Activity Predecessors | Duration(days) A B | Description Build foundation Build walls and ceilings Build the roof Electrical wiring Install windows Put on siding Painting B B CF a) Draw the project diagram, and find the critical path, total duration, and total float and free float for every activity. b) Suppose you are expected to finish the project within 20 days. You find you have to hire more workers in order to shorten the total duration. Please find the minimum cost to achieve the goal. The cost table is shown as follows, Maximum Cost per day of possible Activity reducing the activity reduction in duration activity duration $30k 2 $15k 3 $20k 1 $40k F $30k $40k You can use any method to solve the linear program, e.g., graphical, simplex, excel, etc., except copying. A $20K 2 G 4. [15] Formulate the dual program to a critical path problem (its primal formulation is already given in class), and show that it is also a longest path