We present the production of dual-species Bose-Einstein condensates of $^{39}mathrm{K}$ and $^{87}mathrm{Rb}$. Preparation of both species in the $left| F=1,m_F=-1 rightrangle$ state enabled us to exploit a total of three Fesh-bach resonances which allows for simultaneous Feshbach tuning of the $^{39}mathrm{K}$ intraspecies and the $^{39}mathrm{K}$-$^{87}mathrm{Rb}$ interspecies scattering length. Thus dual-species Bose-Einstein condensates were produced by sympathetic cooling of $^{39}mathrm{K}$ with $^{87}mathrm{Rb}$. A dark spontaneous force optical trap was used for $^{87}mathrm{Rb}$, to reduce the losses in $^{39}mathrm{K}$ due to light-assisted collisions in the optical trapping phase, which can be of benefit for other dual-species experiments. The tunability of the scattering length was used to perform precision spectroscopy of the interspecies Feshbach resonance located at $117.56(2),mathrm{G}$ and to determine the width of the resonance to $1.21(5),mathrm{G}$ by rethermalization measurements. The transition region from miscible to immiscible dual-species condensates was investigated and the interspecies background scattering length was determined to $28.5,a_mathrm{0}$ using an empirical model. This paves the way for dual-species experiments with $^{39}mathrm{K}$ and $^{87}mathrm{Rb}$ BECs ranging from molecular physics to precision metrology.
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