During early phases of wing design, analytic and low-fidelity methods are often used to identify promising design concepts. In many cases, solutions obtained using these methods provide intuition about the design space that is not easily obtained using higher-fidelity methods. This is especially true for aerostructural design. However, many analytic and low-fidelity aerostructural solutions are limited in application to wings with specific planforms and weight distributions. Here, a numerical method for minimizing induced drag with structural constraints is presented that uses approximations that apply to wings with arbitrary planforms and weight distributions. The method is applied to the NASA Ikhana airframe to show how it can be used for rapid aerostructural optimization and design-space exploration. The design space around the optimum solution is visualized, and the sensitivity of the optimum solution to changes in weight distribution, structural properties, wing loading, and taper ratio is shown. The optimum lift distribution and wing-structure weight for the Ikhana airframe are shown to be in good agreement with analytic solutions. Whereas most modern high-fidelity solvers obtain solutions in a matter of hours, all of the solutions shown here can be obtained in a matter of seconds.