Actually, the problem as I posed it is from an engineering point of
view, assuming that a particular constraint dominated the
problem...well, actually I had in mind stating it as wires that would
fit inside some diameter, but that complicated it more than I wanted as
an exercise for this group. Engineers should first ask what the goals
and constraints are, and the space the wires fit into may be one such
constraint. I suppose minimum copper cost would be the smallest wires
(that could handle the required power)!

A starting point for a more complete problem statement from an
engineering point of view might be, "Minimize total system cost,
expressed in net present value, of the system over its operating life,
under a particular set of performance and installation constraints."

Thanks, though, for your consideration of proximity effect. Without
that, I got the same answer as Roy, and appreciated Roy's inclusion of
the basis on which he made the calculation.

I'd point out that for coaxial cable construction, a particular D/d
minimizes the loss for a given D, and a different D/d minimizes the
electric field strength for a given power and therefore maximizes the
power handling capability of the line in the case where the line is
voltage-limited (generally low duty cycle pulse operation), and yet
another D/d minimizes the peak electric field strength for a given
voltage applied to the line. So long as the dielectric loss is
negligible and the dielectric is uniform, all those D/d ratios are
independent of dielectric fill. The D/d which minimizes loss is close
to the D/d which maximizes power handling capability of the line, if
the line is power-dissipation limited, but not exactly so because it
doesn't consider how the center conductor gets rid of its heat. The
minimum attenuation (if the inner and outer conductors are the same
smooth material and skin depth is small compared with the thickness of
each) is for D/d = 3.5911, which as others have pointed out yields
about 76.7 ohms with air dielectric, but if the dielectric is solid
polyethylene, it's about 51 ohms. If the center conductor is smooth
copper and the outer is corrugated aluminum, the minimum-attenuation
D/d increases. If the dielectric is foamed polyethylene, that pushes
the impedance back toward 75 ohms.

Cecil...if the line is limited in power handling by its temperature
rise (which is almost always the case, except for low duty cycle pulses
or line construction that's very different from what we commonly use),
the minimum attenuation configuration will also be the minimum net
dissipation configuration, and therefore close to the optimal power
handling capability. As an example of how cables we commonly use are
thermally limited, consider that solid-dielectric RG-213 at 40C ambient
and at 10MHz is rated at about 2kW. At 50 ohms, that's only 316 vrms
for a CW signal, and RG-213 is rated for use up to 5000 vrms, which
would 250 times as much power (so it better only come in little short
bursts that don't overheat the line). That "power handling is maximum
for Zo=30 ohms" thing is ONLY good if the line is limited by voltage
breakdown, not by temperature rise! It IS useful--in radar systems,
for example--but you must be careful to understand your application.

Cheers,
Tom