Table[
      FindMinimum[
        9/(4*P^2) + 9*4/(8*Q^2) - 3*(z - 0.3)/P - 
          3*z/(2*Q) + (2/
                Q)*((3/2) - (6/10)*(P/Q)^2) - (9/
                10)*(P^2/Q^3), {P, 0.6}, {Q, 4} ],  {z, 3, 15, 
        1}]

{{-7.418177068397157`, {P -> 0.5558124460942176`, 
            Q -> 
              5.7753386452815505`}}, {-14.203595677466033`, {P -> 
              0.40583537387797064`, 
            Q -> 
              2.8796749782550704`}}, {-23.243318967075883`, {P -> 
              0.31958480665692346`, 
            Q -> 
              1.925363747032836`}}, {-34.53539558269188`, {P -> 
              0.26354680592945307`, 
            Q -> 
              1.4496929499766555`}}, {-48.078851791741755`, {P -> 
              0.224215696005836`, 
            Q -> 
              1.163711751340009`}}, {-63.87317552937777`, {P -> 
              0.19509145770526462`, 
            Q -> 
              0.9726071422678133`}}, {-81.91807704779963`, {P -> 
              0.17265877274259986`, 
            Q -> 
              0.8357407051692346`}}, {-102.21338153660612`, {P -> 
              0.15485002867329073`, 
            Q -> 
              0.7328215323019491`}}, {-124.75897775545342`, {P -> 
              0.14036968772451103`, 
            Q -> 
              0.6525762621636505`}}, {-149.55478603545546`, {P -> 
              0.12836985615942859`, 
            Q -> 
              0.5878447886761939`}}, {-176.60076462965677`, {P -> 
              0.11825628301326362`, 
            Q -> 
              0.5351076878895373`}}, {-205.89687350645843`, {P -> 
              0.109619412891012`, 
            Q -> 
              0.4910852250150723`}}, {-237.44308638634695`, {P -> 
              0.1021578334630212`, Q -> 0.4537796629228319`}}}