func = 
      9/(4*P^2) + 9*4/(4*Q^2) - 3*(4 - 0.3)/P - 
        3*(4 - 0.3)/
            Q + (2/
              Q)*(3 - (3/5)*(P/Q)^2)
FindMinimum[
      func, {P, 0.5}, {Q, 1}]

Clear[func];
  
func = 
      9/(4*P^2) + 9*4/(4*Q^2) - 3*(4 - 0.3)/P - 
        3*(4 - 0.3)/Q + (2/Q)*(3 - (3/5)*(P/Q)^2) - 
        6*2*P^2/(5*Q^3)
t = FindMinimum[func, {P, 0.5}, {Q, 1}] 
u = t[[2]];
plot1 = 
      Graphics[{Circle[{0, 0}, P], Circle[{0, 0}, Q], 
            Disk[{0, 0}, 0.12]}]  /.  u
Show[
      plot1, {AspectRatio  ->  Automatic, PlotRange  ->  All, 
        Axes  ->  True, GridLines  ->  Automatic, 
        Frame  ->  True}]
  
Clear[z,  func1];
  
 func1 = 
        9/(4*P^2) + 9*4/(4*Q^2) - 3*(z - 0.3)/P - 
          3*(z - 0.3)/Q + (2/Q)*(3 - (3/5)*(P/Q)^2) - 
          6*2*P^2/(5*
                  Q^3); 

Table[FindMinimum[func1, {P, 0.5}, {Q, 2}], {z, 4, 15}]