  We calculate cross-sections and cross-section ratios of a charm quark
production in association with a $W$ gauge boson at next-to-leading order QCD
using MadGraph and CT10NNLO, CT14NNLO, and MSTW2008NNLO PDFs. We compare the
results with measurements from the CMS detector at the LHC at a center-of-mass
energy of 7TeV. Moreover, we calculate absolute and normalized differential
cross-sections as well as differential cross-section ratios as a function of
the lepton pseudorapidity from the $W$ boson decay. The correlation between the
CT14NNLO PDFs and predictions for $W+$ charm data are studied as well.
Furthermore, by employing the error PDF updating method proposed by the
CTEQ-TEA group, we update CT14NNLO PDFs, and analyze the impact of CMS 7TeV
$W+$ charm production data to the original CT14NNLO PDFs. By comparison of the
$g(x,Q)$, $s(x,Q)$, $u(x,Q)$, $d(x,Q)$, $\bar u(x,Q)$, and $\bar d(x,Q)$ PDFs
at $Q=1.3$ GeV and $Q = 100$ GeV for the CT14NNLO and CT14NNLO+Wc, we see that
the error band of the $s(x,Q)$ PDF is reduced in the region $x<0.4$, and the
error band of $g(x,Q)$ PDF is also slightly reduced in the region $0.01 < x <
0.1$.
