What transfer price paid to production division by marketing

Question

A firm has two semi-autonomous divisions: production and marketing. The production division manufactures a product that is purchased and then resold by the marketing division. The marginal cost functions for the production division and for the value added by the marketing division are defined below.

      MC_P = 2Q_P               MC_M = Q_M
The demand function for the final product is Q^D = 100 - P. Assume that there is no external market for the output of the production division. 

a) How many units should be produced?

b) What transfer price should be paid to the production division by the marketing division?

c) Now suppose there is a perfectly competitive market for the good produced by the production division and the price is $70 per unit.

i)  How many units will the marketing division sell to consumers?

ii) How many units will the production division produce?

How many units will the production division sell to the external market?