BC Aviation is a manufacturer of small single-engine airplanes. The company is relatively small and prides itself on being the only manufacturer of...

BC Aviation is a manufacturer of small single-engine airplanes. The company is relatively small and prides itself on being the only manufacturer of customized airplanes. The company's high standard of quality is attributed to its refusal to purchase engines from outside vendors, and it preserves its competitive advantage by refusing to sell engines to competitors. To achieve maximum efficiency, the company has organized itself into 2 divisions: 1) engine manufacturing division and 2) airplane bodies and assembly division.

Demand for BC Aviation customized planes is given by P = 812000 - 3000Q. The cost of producing engines is TCe = 5000Qe^2, and the cost of assembling airplanes is TCa = 12000Qa

a. What the problems would occur if the managers of each division were given incentives to maximize each  division's profit separately?

b. What price should the owners of BC Aviation set for engines in order to avoid this problem and maximize overall profits?

c. What price will be charged by the BC Aviation to maximize the profits?

Thanks!