Mito Corporation has a Castings Division that does casting work of various types. The company's Machine Products Division has asked the Castings Division to provide it with 25,000 special castings each year on a continuing basis. The special castings would require $15 per unit in variable production costs. The Machine Products Division has a bid from an outside supplier of $32 per unit for the castings.

In order to have time and space to produce the new castings, the Castings Division would have to cut back production of another casting: the NN2, which it presently is producing. The NN2 sells for $33 per unit, and requires $18 per unit in variable production costs. Boxing and shipping costs of the NN2 are $5 per unit. Boxing and shipping costs for the new special casting would be only $2 per unit. The company is now producing and selling 200,000 units of the NN2 each year. Production and sales of this casting would drop by 15% if the new casting is produced.

Required: 

a) What is the range of transfer prices within which both the divisions' profits would increase as a result of agreeing to the transfer of 25,000 castings per year from the Castings Division to the Machine Products Division?

b) Is it in the best interests of Mito Corporation for this transfer to take place? If so, by how much would the profit of the company increase?