Weller Industries is a decentralized organization with six divisions. The company$$s Electrical Division $($which is operating at capacity$)$ sells this fitting to its regular customers for $$7\mathrm{.}50$ each; the fitting has a variable manufacturing cost of $$4\mathrm{.}25.$

The company$$s Brake Division has asked the Electrical Division to supply it with a large quantity of X$52$ fittings for only $$5$ each. The Brake Division, which is operating at $50\%$ capacity, will put the fitting into a brake unit that it will produce and sell to a large commercial airline manufacturer. The cost of the brake unit being built by the Brake Division follows:

Purchased parts $($from outside vendors$)$ $$22\mathrm{.}50$

Electrical fitting X$525\mathrm{.}00$

Other variable costs $14\mathrm{.}00$

Fixed Overhead and Administration $8\mathrm{.}00$

TOTAL cost per brake unit $$49\mathrm{.}50$

Although the $$5$ price for the X$52$ fitting represents a substantial discount from the regular $$7\mathrm{.}50$ price, the manager of the Brake Division believes the price concession is necessary if his division is to get the contract for the airplane brake units. He has heard $$through the grapevine$$ that the airplane manufacturer plans to reject his bid if it is more that $$50$ per brake unit. Thus, if the Brake Division is forces to pay the regular $$7\mathrm{.}50$ price for the X$52$ fitting, it will either not get the contract or it will suffer a substantial loss at a time when it is already operating at only $50\%$ of capacity. The manager of the Brake Division argues that the price concession is imperative to the well$-$being of both his division and the company as a whole.

Weller Industries uses return on investment to measure divisional performance.

Assume that the airplane brakes can be sold for $$50$

$1.$ Calculate the acceptable lowest and highest transfer prices if the Electrical Division is operating at its full capacity.

$2.$ Discuss whether the Electrical Division and the Brake Division could find an agreeable transfer price that would benefit both the divisions. Explain why or why not the two divisions may come to an agreement. If not, suggest possible remedies for the disagreement.