Consider an executive jet transport patterned after the Cessna $560.$ The airplane is cruising at a velocity of $520$ mph at an altitude of $33,000ft,$ where the ambient air density is $7\mathrm{.}9656{10}^{-4}$ slug$/f{t}^3.$ The weight and wing planform areas of the airplane are $17,000lb$ and $350f{t}^2,$ respectively. The drag coefficient at cruise is $0\mathrm{.}015.$ Calculate the lift coefficient and the lift$-$to$-$drag ratio at cruise. The Cessna can fly at a max speed of $550$ mph and requires at least $120$ mph to generate any lift. Calculate the maximum thrust generated by the Cessna and the maximum lift coefficient. Also calculate the maximum drag, maximum lift to maximum drag ratio $(\frac{L_{\text{m}\text{a}\text{x}}}{D_{\text{m}\text{a}\text{x}}})$ and the maximum lift to drag ratio $(\frac{C_L}{C_D}{)}_{\text{m}\text{a}\text{x}}$

$(20$ points$)$