How do i setup for this function?

I know this is pretty simple thing but I just started using matlab so don`t know how to set up variables for this one.

X=(0.5454*Mu+0.015*Kbf)/(Kbf-0.1818*Mu) 
Y=((0.4545*Mu)+0.0155*(1-Kbf))/((1-Kbf)+(0.1818*Mu))

and X<Y

For Mu=0.2,0.4,0.6,0.8,

I need to find min Kbf value. How can I set this up?

Answer 1

[Roger Stafford]

If we call d = Y-X, by plotting d as a function of Kbf it is immediately evident that Kbf attains a minimum when d is zero. (Strictly speaking, if we require that Y>X, then Kbf cannot attain a minimum, so I will change your condition to Y>=X.) Setting d equal to 0, the resulting equation in Kbf can be converted (after some effort) to the following equivalent quadratic equation:

   -0.0005*Kbf^2+(0.9849909*Mu+0.0155)*Kbf-0.72718182*Mu^2-0.0028179*Mu = 0

Calling its coefficients A, B, and C

   A = -0.0005;
   B = 0.9849909*Mu+0.0155;
   C = -0.72718182*Mu^2-0.0028179*Mu;

the smaller of the two roots can be expressed as:

   Kbf = -2*C/(B+sqrt(B^2-4*A*C));

which is the solution to your problem after you plug in the value of Mu.