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The measurement and improvement of task agility, the ability of a manipulator to effectively handle multiple task types, has become increasingly important in the manufacturing industry as efforts are made to design more versatile and efficient factories. Task agility is crucial to the performance of kinematically redundant manipulators in complex manufacturing workspaces that involve several physical motion impediments and conservative dynamic actuation constraints, and which are used to complete a wide variety of manufacturing operations. Manipulator morphology and workspace layout optimizations offer robust, long term solutions to the problem of improving task agility, but the cost of redevelopment or redeployment is typically prohibitive. Manipulator placement optimization is a more economically feasible and practical solution that is amenable to short term implementation. In this paper we propose the use of a multiobjective weighted isotropy measure as a task agility metric and submit it as the basis for optimizing the placement of redundant manipulators in a complex, multitask workspaces. We describe the formulation of this measure, how it factors motion impedance into kinematic dexterity, and the advantages of this measure over previous task agility measurement methods. We demonstrate its efficacy in improving task agility by optimizing manipulator base placement to achieve collision-free motion and reduced maximum torques across an entire set of disparate manipulation tasks.