A Low-Pressure Micro-resistojet (LPM) is a type of in-space electrothermal propulsion system for satellites that works by heating low-pressure (50 to 300 Pa) fluid flowing through microchannels/slots (typically <1 mm diameter) using resistive heating elements like thin-film Molybdenum. This thesis delineates a response surface based method to explore and optimize the cross-sectional design of microchannels, which, as documented in literature, have so far only been either rectangular or circular in shape. Experimental studies place the efficiency of LPM systems at 25% which can be increased to 30% by reducing heat losses from the heat exchanger to the plenum. The concept is still in its early stages of development and therefore offers plenty of opportunities in the improvement of the propulsion system whether it be regarding the choice of propellant, design of propellant management system, choice of thruster materials or the design of the microchannels, which is the focus of this thesis. Usage of Response Surface Methodology (RSM) to optimize the design of a microchannel for greater thrust efficiency requires the following steps: Design of Experiment (DoE) run to select samples from the design space, performing experiments to evaluate the performance of selected samples, building a response surface (or surrogate model) from the generated data and finally using an optimization algorithm to find a high-efficiency design. In this thesis, these steps were performed using (respectively): Sobol Sequences, Direct Simulation Monte Carlo (DSMC) method using Sparc Industries' VSTRAP software, Convolutional Neural Network (CNN) and Genetic Algorithm (GA). As a case study, the optimization was performed for Argon as the propellant, inlet pressure of 50 Pa, inlet temperature of 300 K and microchannel wall temperature of 600 K. The number of design parameters were set as 8 though the base geometry supports higher numbers as well. Using Sobol sequences to determine parametric values, 512 designs (termed polar designs) were generated. After DSMC simulations (validated with an experimental study in literature), the best performing design was found to have a thrust efficiency of 0.7019. 512 Rectangular designs were generated as well among which the best performing design had a thrust efficiency of 0.6566. From this dataset, the main takeaway is that the thrust efficiency peaks at a certain slot area and that small areal rectangular slots, common in literature, are not as efficient as broader slots with higher cross-sectional area (up to a limit). The CNN was trained on the polar dataset (CNN1) as well as the combination of both datasets (CNN2) to predict thrust efficiency from slot images. The predictions were, on average, within 10% from the simulation results. A GA run with 8-parameter geometry and with CNN1 as the response surface resulted in an optimum design with a thrust efficiency of 0.732. With CNN2, the optimized efficiency for 8-parameter and 15-parameter geometry was 0.7281 and 0.7455 respectively. However, on simulating the GA results it was found that CNN1 and CNN2 had overestimated the thrust efficiency by 11%. Thus in this case study, the most thrust efficient design is the best one from the polar dataset. The conclusion drawn is that a high number of designs generated using Sobol Sequences are enough to find the best performing design for a given set of input conditions i.e. choice of propellant, inlet pressure and temperature, and heaterchip temperature. As it seems that there is a strong correlation between slot area and performance, the number of designs to be generated can be based on whether it spans the allowable minimum to the allowable maximum area set by the designer. However, if the correlation between slot area and performance is not found after a DoE run for a different set of input conditions, then a CNN would have to be trained and used by the GA for design optimization. The thesis concludes with a design recommendation for the shape of a microchannel that may on experimental testing result in a high performing thruster. Improvement in LPM technology will further the capabilities of PocketQube satellites (5 x 5 x 5 cm^3 form factor) and also of large satellites for which it could function as precise attitude control thrusters. Low pressure operation allows for a compact and lightweight propellant management system and the thruster's high thrust-to-power ratio gives it a major advantage over competing propulsion systems such as hall-effect and electrospray thrusters.