$.$ Norton Industries is installing a new computer system. The activities, the activity times, and the project network are as follows: Activity Time Activity Time A $3$ E $4$ B $6$ F $3$ C $2$ G $9$ D $5$ H $3$ Start A E F D G C B H Finish The critical path calculation shows B$-$D$-$E$-$F$-$H is the critical path, and the expected project completion time is $21$ weeks. After viewing this information, management requested overtime be used to complete the project in $16$ weeks. Thus, crashing of the project is necessary. The following information is relevant: Time $($weeks$)$ Cost $($$$)$ Activity Normal Crash Normal Crash A $319001700$ B $6320004000$ C $215001000$ D $5318002400$ E $4315001850$ F $3130003900$ G $9480009800$ H $3210002000$ a$.$ Formulate a linear programming model that can be used to make the crashing decisions for this project. b$.$ Solve the linear programming model and make the minimum cost crashing decisions. What is the added cost of meeting the $16-$week completion time? c$.$ Develop a complete activity schedule based on the crashed activity times.