$17$ A project management organization is preparing a network for one of the projects that it has recently bid for. The client demands that the project needs to be completed and delivered at its site by Week $25.$ The organization has identified the list of activities to be performed and estimated the duration of each of the activities. The details are given in the table below. Use this information to draw a network and help the organization answer the following questions.

Activity

Predecessor

Duration $($weeks$)$

$8$

A

B

A

$3$

C

A

$6$

D D

A

$4$

E

B

$5$

F

B

$4$

G

H

C$,$E

D

$6$

$1$

$6$

J

$6$

K

D

$4$

G$,$H$,$I

J$,$K

$3$

L

$3$a$)$ Will the organization be able to meet the customer's deadline of $25$ weeks?b$)$ If the organization cannot, identify the set of activities that need to be considered for a possible reduction in duration.c$)$ If the cost of reduction of duration is INR $10,000$ per week and the organization will have to pay a penalty of INR $7,000$ per week of delay in completion in addition to paying a fixed amount of INR $20,000,$ what will your recommendation be to the organization with respect to reducing the duration?