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 $6,000$ special parts each year. The special parts would require $$21$ per unit in variable production costs.

The Machine Division has a bid from an outside supplier for the special parts at $$31\mathrm{.}20$ per unit. In order to have time and space to produce the special'part, the Parts Divistion would have to cut back production of another part$-$the QR$4$ that it presently is producing. The QR$4$ sells for $$40$ per unit and requires $$20$ per unit in variable production costs. Packaging and shipping costs of the QR$4$ are $$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 $30,000$ 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 the transfer of $6,000$ special parts per year from the Parts Division to the Machine Division?

Note: Round your final answers to $2$ decimal places.

Answer is complete but not entirely correct.

Range of transfer prices:

$$ Transfer

price $$