Fyodor Corporation has a Parts Division that does work for other Divisions in the company as well as for outside customers. The company's Machine Division has asked the Parts Division to provide it with $7,200$ special parts each year. The special parts would require $$27$ per unit in variable production costs.

The Machine Division has a bid from an outside supplier for the special parts at $$39\mathrm{.}30$ per unit. In order to have time and space to produce the special part, the Parts Division would have to cut back production of another part$-$the QR$4$ that it presently is producing. The QR$4$ sells for $$52$ per unit, and requires $$26$ per unit in variable production costs. Packaging and shipping costs of the $QR4$ are $$2$ per unit. Packaging and shipping costs for the new special part would be only $$0\mathrm{.}50$ per unit. The Parts Division is now producing and selling $36,000$ units of the QR$4$ each year. Production and sales of the QR$4$ would drop by $5\%$ if the new special part is produced for the Machine Division.

Required:

a$.$ What is the range of transfer prices within which both the Divisions' profits would increase as a result of agreeing to theriransfer of $7,200$ special parts per year from the Parts Division to the Machine Division? $($Round your final answers to $2$ decimal places.$)$

Range of transfer prices:

$$ Transfer price $$

b$.$ Is it in the best interests of Fyodor Corporation for this transfer to take place?

Yes

No