A company must decide between scrapping or reworking units that do not pass inspection. The company has $13,000$ defective units that have already cost $$132,000$ to manufacture. The units can be sold as scrap for $$35,100$ or reworked for $$61,100$ and then sold for $$111,800.$

$($a$)$ Prepare a scrap or rework analysis of income effects.

$($b$)$ Should the company sell the units as scrap or rework them?