Problem $1(15$ pts$)$

A signal arm carries two traffic signals and a sign, as shown. The signals and sign are rigidly attached to the arm. Each traffic signal is $0\mathrm{.}2m^2$ in frontal area and weight $210N.$ the sign weighs $60\frac{N}{m^2}.$ The design wind pressure is $575\frac{N}{m^2}.$ The maximum moment that the connection between the arm and pole can withstand due to wind is $6000N-m$ and the maximum permitted moment due to the loads is $4000N-m.$ As limited by moment on the connection, what is the maximum area of the sign?

$($A$),1\mathrm{.}04m^2$

$($B$),1\mathrm{.}15m^2$

$($C$),5\mathrm{.}65m^2$

$($D$),8\mathrm{.}03m^2$