An engineer is designing a structural beam that contains a lengthwise conduit that will be used for routing cable. As shown, the cross section of the beam has the dimensions aa $=0\mathrm{.}730$ ftft $,$ bb $=1\mathrm{.}06$ ftft $,$ cc $=0\mathrm{.}220$ ftft $,$ and dd $=0\mathrm{.}360$ ftft $.($Figure $1)$The beam's centroid is located at point C $(3\mathrm{.}02102$ ftft $,2\mathrm{.}08102$ ftft $).$ The engineer wishes to determine the beam's principal moments of inertia and the orientation of the principal axes using Mohr's circle. First, find the beam's moment of inertia and product of inertia. What are the beam's moments of inertia, IxIx and IyIy, about the centroidal x$\text{'}$ and y$\text{'}$ axes, respectively? What is the beam's product of inertia about its centroid?

IxIx, IyIy, IxyIxy $=$