A firm sells specialized electronic computers. Each of the computers has a unique chip produced at a California plant at cost of Cw(Qc)=Q^2 c
[C subscript w *(Q subscript c)=Q squared subscript c.]
Once produced, the chips are shipped to the firm's new jersey east coast plant where the computers are then assembled, packaged and shipped to market at a cost of Ce(Q)=200Q. [C sub e * Q=200Q]
Demand was recently estimated for the computers and found to be P=5000-Q.
Given this,
1. what is optimal output for the computers?
2. what is optimal transfer price between the two plants?