Modify your formulation for Exercise 1 to find the maximum permissable loads (P1 and P2) s...

Modify your formulation for Exercise 1 to find the maximum permissable loads (P1 and P2) such that the force exerted at supports 1 and 2 are equal.

Exercise 1

Consider the simply supported beam shown below:

The load-carrying capacities of supports 1 and 2 are 12 and 19 kips, respectively. The beam itself can withstand a bending moment of 65 kip-feet, and the maximum stress created by any loading is assumed to occur at one of the load points (a or b).

Formulate a linear program that will determine the maximum possible loads (P1 and P2) that this system can carry. Solve your model using the simplex algorithm, and summarize each simplex pivot by showing the appropriate basis representation or simplex tableau.