This paper presents an analytical research study to improve the aerostructural performance of an unmanned medium altitude long endurance aircraft using the adaptive wing concept. Aerodynamic drag and wing root loads are minimized by optimal scheduling of multiple trailing edge flaps located on the wing. A trim optimization process is developed specifically for this purpose. The aeroelastic model is based on finite element formulation for the structure and doublet lattice method for the aerodynamics. A nonlinear numerical lifting line method is used, in combination with airfoil wind tunnel data, to estimate the induced and total drags. Results are presented for the current aircraft configuration and a more flexible proposed configuration, thereby providing an uncommon perspective on the effect of flexibility on the adaptive wing. For example, the benefits of optimal flap deployment turn out to be greater for the flexible aircraft than for the rigid one. It is hoped that this work and its insights will also aid the multidisciplinary design optimization of future aircraft.