Pure Comfort manufactures and sells mattresses with adjustable air

chambers. Pure Comfort has been producing and selling

approximately $500,000$ units per year. Each units sells for $$600,$ and

there are no variable selling, general, or administrative costs. The

company has been approached by a foreign supplier who wishes to

provide the air compressor component for $$75$ per unit. Total annual

manufacturing costs, including air compressors, is as follows:

If Pure Comfort outsources the air compressor, it is expected that:

Direct materials will be reduced by $20\%,$ direct labor will be reduced by $30\%,$ and variable factory overhead will be reduced by $25\%.$

There will be no reduction in fixed factory overhead.

$($a$)$ Should Pure Comfort outsource the air compressor?