  We investigate a Geometric Brownian Information Engine (GBIE) in the presence
of an error-free feedback controller that transforms the information gathered
on the state of Brownian particles entrapped in monolobal geometric confinement
into extractable work. Outcomes of the information engine depend on the
reference measurement distance $x_m$, feedback site $x_f$ and the transverse
force $G$. We determine the benchmarks for utilizing the available information
in an output work and the optimum operating requisites for best work
extraction. Transverse bias force ($G$) tunes the entropic contribution in the
effective potential and hence the standard deviation ($\sigma$) of the
equilibrium marginal probability distribution. We recognize that the amount of
extracted work reaches a global maximum when $x_f = 2x_m$ with $x_m \sim
0.6\sigma$, irrespective of the extent of the entropic limitation. Because of
the higher loss of information during the relaxation process, the best
achievable work of a GBIE is lower in an entropic system. The feedback
regulation also bears the unidirectional passage of particles. The average
displacement increases with growing entropic control and is maximum when $x_m
\sim 0.81\sigma$. Finally, we explore the efficacy of the information engine, a
quantity that regulates the efficiency in utilizing the information acquired.
With $x_f=2x_m$, the maximum efficacy reduces with increasing entropic control
and shows a cross over from $2$ to $11/9$. We discover that the condition for
the best efficacy depends only on the confinement length scale along the
feedback direction. The broader marginal probability distribution accredits the
increased average displacement in a cycle and the lower efficacy in an
entropy-dominated system.
