Air Comfort Electronics Produces Small, Electric, Victorian-Reproduction Fans for Home

Air Comfort Electronics produces small, electric, Victorian-reproduction fans for home and office use. The final product division of the company manufactures all parts of the fan except the electric motor, and then assembles, packages and distributes the product. The fan motors are produced by a separate division of the firm called Westside Armature Works.
Westside could sell the motors in the open market to a number of other fan and appliance manufacturers at a standard price of $2.50. There is vigorous competition in the electric motor industry and it is unlikely that, for the size and type motor needed for the fan, any but the going price can be obtained.
Management has determined that the demand curve in quantity sold per month for its most popular model, the Casa-Frio model is:
Q_c = 8,250 - 100P_c, so that MR_c = 82.5 - .02Q_c)
while Air Comfort's marginal cost for the Casa-Frio fan, excluding the cost of the display module is:
MC_c = .003_c
In addition, management has determined that the marginal cost for the electric motors is:
MC_m = .0005Q_m
a. At what final product price and rate of output will the firm maximize profit?
b. How much of the transfer product should be produced?
c. Should the final product division obtain all of its motors for the fan from Westside Armature Works? Why or why not?