  We present the results of extensive modeling of the spectral energy
distributions (SEDs) of the closest blazar (z=0.031) Markarian 421 (Mrk 421)
during a giant outburst in February 2010. The source underwent rapid flux
variations in both X-rays and very high energy (VHE) gamma-rays as it evolved
from a low-flux state on 2010 February 13-15 to a high-flux state on 2010
February 17. During this period, the source exhibited significant spectral
hardening from X-rays to VHE gamma-rays while exhibiting a "harder when
brighter" behavior in these energy bands. We reproduce the broadband SED using
a time-dependent multi-zone leptonic jet model with radiation feedback. We find
that an injection of the leptonic particle population with a single power-law
energy distribution at shock fronts followed by energy losses in an
inhomogeneous emission region is suitable for explaining the evolution of Mrk
421 from low- to high-flux state in February 2010. The spectral states are
successfully reproduced by a combination of a few key physical parameters, such
as the maximum $\&$ minimum cutoffs and power-law slope of the electron
injection energies, magnetic field strength, and bulk Lorentz factor of the
emission region. The simulated light curves and spectral evolution of Mrk 421
during this period imply an almost linear correlation between X-ray flux at
1-10 keV energies and VHE gamma-ray flux above 200 GeV, as has been previously
exhibited by this source. Through this study, a general trend that has emerged
for the role of physical parameters is that, as the flare evolves from a low-
to a high-flux state, higher bulk kinetic energy is injected into the system
with a harder particle population and a lower magnetic field strength.
