Planktonic ecosystems provide a key mechanism for the transfer of CO2 from the atmosphere to the deep ocean via the so-called "biological pump". Mathematical models of these ecosystems have been used to predict CO2 uptake in surface waters, and more recently have been embedded in global climate models. While the equilibrium properties of these models are well studied, less attention has been paid to their response to external perturbations, despite the fact that as a result of the variability of environmental forcing such ecosystems are rarely, if ever, in equilibrium. Human induced perturbations to these ecosystems, namely the addition of limiting nutrients (e.g. iron) to areas where nitrate is plentiful to accelerate the biological pump, have been proposed as a solution to reduce atmospheric CO2. Linear theory is used to determine the structure of "unit-norm" perturbations (size in mmol N m^-3) to state variables of an ecosystem model in steady state, describing Ocean Station P (50N 145W) in summer, that optimize either instantaneous export flux of organic matter at fixed times or integrated export as the ecosystem relaxes towards equilibrium. For all perturbations, the flux to higher trophic levels is the primary contributor to export flux, the contribution of aggregation is negligible, and (sinking) detritus increases significantly in the transient dynamics. Two perturbations considered optimize instantaneous export flux; both perturbations synchronize P1 and Z1 relative to their predator prey cycle, resulting in a maximum instantaneous export flux of 4.4 mmol N m^-2 d^-1, and also increased integrated export above that at steady state (6 g C m^-2 over 150 days). An increase in larger phytoplankton (P2), representing diatoms, results in the highest integrated export (7 g C m^-2). The perturbations in which P2 persist the longest give the highest integrated export, and these perturbations are primarily increases in P2. The additional integrated export in response to a proportional increase to steady state concentrations of both large and small phytoplankton is positive, but much lower than the optimal perturbations. However, the additional integrated export in response to an increase in only P1 is negligible. The linear and nonlinear ecosystem and export responses to two perturbations are compared; for perturbations of magnitude 0.5 mmol N m^-3, the linearization of the ecosystem dynamics, rather than of the export flux, is the primary cause for differences between the fully linear and fully nonlinear cases.