We report measurements of the charge-separated W+(−)→e+(−)+νe(ν¯e) and Z/γ∗→e+e− production cross sections at mid-rapidity in proton-proton collisions at s√=500  GeV. These results are based on 13.2  pb−1 of data recorded in 2009 by the STAR detector at RHIC. Production cross sections for W bosons that decay via the eν channel were measured to be σ(pp→W+X)⋅BR(W+→e+νe)=117.3±5.9(stat)±6.2(syst)±15.2(lumi)  pb, and σ(pp→W−X)⋅BR(W−→e−ν¯e)=43.3±4.6(stat)±3.4(syst)±5.6(lumi)  pb. For Z/γ∗ production, σ(pp→Z/γ∗X)⋅BR(Z/γ∗→e+e−)=7.7±2.1(stat)+0.5−0.9(syst)±1.0(lumi)  pb was measured for di-lepton invariant masses me+e− between 70 and 110  GeV/c2. First measurements of the W cross section ratio, σ(pp→W+X)/σ(pp→W−X), at √s=500  GeV are also reported. Theoretical predictions, calculated using recent parton distribution functions, are found to agree with the measured cross sections.