Business Unit X produces a widget product that can be sold either to external customers or internally to Business Unit Y$.$ Business Unit Y is currently purchasing $20,000$ widgets from an external supplier for $$47$ per unit. Both Business Unit X and Business Unit Y are evaluated as profit centers. Production and sales data for Business Unit X are provided below.

Business Unit X:

Capacity in units $100,000$

Number of units being sold to external customers $100,000$

Selling price per unit to external customers $$50$

Variable costs per widget $$30$

Fixed costs per unit $($based on capacity$)$ $$8$

Assuming that variable costs of $$2$ per widget can be avoided if an internal transfer takes place, should Business Unit X transfer widgets to Business Unit Y$?$ If so$,$ what range of transfer prices is acceptable? $(4\mathrm{.}5$ pts$)$