Maximum weight for suspended cable system with capacity limits

[bsaab]

Homework Statement

In a certain structure, the cables C1, C2, and C3 (Figure) can each carry a weight of 100kg, and C4, C5, and C6 can each carry 50kg. Weights are suspended at R, S, and T.

What is the maximum total weight the structure can carry?

PS1: (Ignore the weight of the structure itself).
PS2: (The distances are in red).

It's important to tell that this problem requires a linear programming solution but I just want to know about the physics concepts behind the problem.

Any help would be good for me.

Thanks in advance!

Homework Equations

Here goes the figure

[PLAIN]http://img692.imageshack.us/img692/3176/systemd.png

The Attempt at a Solution

 

[JaredJames]

Do you know how to calculate the forces through the structure when the weights are applied at each point?

 

[Beaker87]

To solve this, you want to work up from the bottom, finding the torque applied to each support, and the force the support needs to apply in order to supply that much torque.

For example:

$$\frac{3T}{4} = C6 \leq 50$$

and

$$\frac{S+2C6}{3} = C3 \leq 100$$



Then perform any substitutions that you can
From the above examples:

$$\frac{S+2\frac{3T}{4}}{3} = C3 \leq 100$$

 

[bsaab]

Beaker

Your method is correct, the system are in rest so the torque applied to each support has to be zero.

Im really thankful!