func = 
      9/(4*P^2) + 9*4/(8*Q^2) - 3*(3 - 0.3)/P - 
        3*3/(2*Q) + (2/
              Q)*((3/
                  2) - (3/10)*(P/Q)^2)
FindMinimum[
      func, {P, 0.5}, {Q, 
        1}]


  
func = 
      9/(4*P^2) + 9*4/(8*Q^2) - 3*(3 - 0.3)/P - 
        3*3/(2*Q) + (2/Q)*((3/2) - (3/10)*(P/Q)^2) - 
        6*P^2/(5*Q^3)
FindMinimum[func, {P, 0.5}, {Q, 1}]
plot1 = 
      Graphics[{Circle[{0, 0}, 0.5558], Circle[{0, 0}, 5.8084], 
          Disk[{0, 0}, 0.12]}]
Show[plot1, {AspectRatio -> Automatic}]

func = 
      9/(4*P^2) + 9*4/(8*Q^2) - 3*(z - 0.3)/P - 
        3*z/(2*Q) + (2/
              Q)*((3/2) - (3/10)*(P/Q)^2) - (6/5)*
          P^2/Q^3

Table[FindMinimum[func, {P, 0.5}, {Q, 1}], {z, 3, 15}]