Suppose Airboeing is the sole manufacturer of airplanes; demand for Airboeing airplanes is given by QA (PA ) = 100 P_a where P_a is the price of a plane. To produce a plane, it takes one plane body, which Airboeing produces at constant cost c_a = 50, and two engines specifically made by Pratt Royce. Denote PE the price that Pratt Royce charges for an engine. So Airboeing's cost of manufacturing a plane is c_a + 2P_e ; Airboeing takes PE as given. Pratt Royce produces engine at constant marginal cost c_e = 15.

a) [5pts] Airboeing takes PE as given. Solve Airboeing's profit maximization problem. How many planes Q_A^M does Airboeing produce? At what price P_A^M do they sell? What is Airboeing mark-up? What is Airboeing profit M_A ? (Hint: your answers will depend on P_E .)