A high-current, parallel-plate, super-capacitor for a satellite has a manufacturing and space restrictions that require the negative plate to be exactly 1.5 mm thick, the positive plate 1 mm thick, and the dielectric between them 2 mm thick, and require all three to have a length of 5 cm. Having these layers stacked along their thickness (and centred in width), we can manufacture each to any width up to a maximum of 3 cm, i.e. all three can have different widths, or the same width, or 2 of equal width and one different, AS LONG AS each is no more than 3 cm wide.
The dielectric has a relative permittivity of 12 and a density of 2.3 g cm-3. The plates each have a density of 8.2 g cm-3.
The client needs you to determine the set of 3 widths (for each plate and the dielectric) that will maximize the capacitance of this high-current, parallel-plate, super-capacitor. The client emphasized adherence to the geometry restrictions above, and they also mentioned that the total capacitor mass must not exceed 6 g before running to some other meeting.