1. ## Linear Programming Problem

Hi all, I am trying to teach myself some linear programming and have become stuck with this quesion

Lets Suppose a large construction project has been broken down into 6 activities. The times to complete the activities along with the necessary preceding activities are shown in the following table.

 Activity Preceding Activity Duration (Weeks) A - 50 B A 30 C A 20 D A 40 E B,C 50 F B 40 G D,E,F 60

Activities E and F will require external consultants to conduct the work and so times for these
activities are based on preliminary estimates from the contractors. The agreed completion
time for the project has to be within 160 weeks.

a) Formulate this situation as a linear programming problem, where the aim is to complete the project in the shortest possible time.

Thanks

2. ## Re: Linear Programming Problem

Hint: the shortest possible time is 190 weeks (which is 1165 days past the desired completion point).

3. ## Re: Linear Programming Problem

I apologize, all units are all meant to be in weeks

Indeed I may see that this is a Shortest path problem, and that the shortest possible time is 190 weeks. This is how I have formulated it as a linear program so far

A+50 <= B
A+50 <= C
A+50 <= D
B+30 <= E
B+30 <= F
C+20 <= E
D+40 <= G
E+50 <= G
F+40 <= G

A=0
B,C,D,E,F,G >= 0

4. ## Re: Linear Programming Problem

I am not quite sure what a linear program is supposed to look like, so that was as helpful as I could be.

5. ## Re: Linear Programming Problem

No Problem, that you for your help though