The kinematic dependences of the relative production rates, $f_{Lambda_b^0}/f_d$, of $Lambda_b^0$ baryons and $bar{B}^0$ mesons are measured using $Lambda_b^0 rightarrow Lambda_c^+ pi^-$ and $bar{B}^0 rightarrow D^+ pi^-$ decays. The measurements use proton-proton collision data, corresponding to an integrated luminosity of 1 fb$^{-1}$ at a centre-of-mass energy of 7 TeV, recorded in the forward region with the LHCb experiment. The relative production rates are observed to depend on the transverse momentum, $p_T$, and pseudorapidity, $eta$, of the beauty hadron, in the studied kinematic region $1.5 < p_T < 40$ GeV/$c$ and $2 < eta < 5$. Using a previous LHCb measurement of $f_{Lambda_b^0}/f_d$ in semileptonic decays, the branching fraction $mathcal{B}(Lambda_b^0 rightarrow Lambda_c^+ pi^-) = Big( 4.30 pm 0.03 ,, ^{+0.12}_{-0.11} pm 0.26 pm 0.21 Big) times 10^{-3}$ is obtained, where the first uncertainty is statistical, the second is systematic, the third is from the previous LHCb measurement of $f_{Lambda_b^0}/f_d$ and the fourth is due to the $bar{B}^0 rightarrow D^+ pi^-$ branching fraction. This is the most precise measurement of a $Lambda_b^0$ branching fraction to date.
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