A converging-diverging nozzle receives air from a tank at \(100 \mathrm{psia}\) and \(600^{\circ} \mathrm{R}\). The pressure is 28.0 psia immediately preceding a plane shock that is located in the diverging section. The Mach number at the exit is 0.5 and the flow rate is 10 \(\mathrm{lbm} / \mathrm{sec}\). Determine:

(a) The throat area.

(b) The area at which the shock is located.

(c) The outlet pressure required to operate the nozzle in the manner described above.

(d) The outlet area.

(e) The design Mach number.