How to solve max load of P in Matlab?

The equations governing the forces on the beam shown below are as follows:

F_ax=0

P=F_ay+F_by

P=(5.*F_by)./10

We want to determine the maximum load, P, which will result in a load at the roller, F_by, which does not exceed 500 lb. 

Write a Matlab program which uses the above system of equations to determine the maximum force P which results in vertical force on the roller, F_by of between 499 lb and 500 lb. Your approach should repetitively solve the above system of equations until the desired result is obtained.

This is the code I have, but I don't know where to go next:

F_ax=0

F_by<=500 %lbs
F_by>=499 %lbs

P=F_ay+F_by

P=(5.*F_by)./10

Answer 1

[bym]

So, when I see a problem statement that says "solve the above system of equations" I think of formulating the equations in matrix form. The coefficient matrix for the equations involving P is

    c =

      1.0000    1.0000
           0    0.5000

when I see a problem statement that says "... until the desired result is obtained", I think of a loop structure

doc while

when the problem statement says "[repetitively] solve..." The repetition is taken care of in the loop, but solving usually involves finding the unknowns. this often involves mldivide

doc mldivide

As you can see, I haven't given you the direct answer, but areas to explore in solving your homework problem

[Katie]

How did you get c to answer in matrix form? And my professor hasn't gone over doc while of doc mldivide. We have just whose while and for loops and the expectations are to not use the short cuts. What is the difference of a doc while and a while loop?

[bym]

doc command is just a way of getting to the help documentation from the command line. As far a getting the coefficient matrix, it is a matter of writing out the equations and putting the coefficients into a matrix, e.g.

1*F_ay+1*F_by = P

0*F_ay+.5*F_by = P

equals

[1,1;0,.5]*[F_ay;F_by] = [P;P]