$(60$ points$)$ The duration and cost for each activity in normal and crash situations for a project

network are shown below. Answer the following questions.

$(20$ points$)$ Use marginal analysis to find the least expensive way to crash $($reduce the

duration of$)$ activities so the project duration is reduced to $13$ weeks from the normal $15$

weeks.

$(20$ points$)$ Formulate a linear programming $($LP$)$ problem to find the least expensive way

to crash activities so that project duration is reduced to $11$ weeks.

$(20$ points$)$ Use Excel Solver to solve the formulated LP problem in $2)$ to obtain an

optimal solution.