Collyer Products Inc. has a Valve Division that manufactures and sells a standard valve as follows:

Capacity in units $10,000$

Selling price to outside customers on the intermediate market $ $15$

Variable costs per unit $ $8$

Fixed costs per unit $($based on capacity$)$ $ $5$

The company has a Pump Division that could use this valve in the manufacture of one of its pumps. The Pump Division is currently purchasing $10,000$ valves per year from an overseas supplier at a cost of $$14$ per valve.

Required:

$1.$ Assume that the Valve Division has ample idle capacity to handle all of the Pump Division's needs. What is the acceptable range, if any, for the transfer price between the two divisions?

$2.$ Assume that the Valve Division is selling all that it can produce to outside customers on the intermediate market. What is the minimum transfer price acceptable to the Valve Division for transfers to the Pump Division?

$3.$ Assume again that the Valve Division is selling all that it can produce to outside customers on the intermediate market. Also assume that $$2$ in variable expenses can be avoided on transfers within the company, due to reduced selling costs. What is the acceptable range, if any, for the transfer price between the two divisions?

$4.$ Assume the Pump Division needs $20,000$ special high$-$pressure valves per year. The Valve Division's variable costs to manufacture and ship the special valve would be $$10$ per unit. To produce these special valves, the Valve Division would have to reduce its production and sales of regular valves from $100,000$ units per year to $70,000$ units per year. As far as the Valve Division is concerned, what is the lowest acceptable transfer price? $($Round your answer to $2$ decimal places.$)$