Hip Manufacturing produces denim clothing. This year it produced $3,340$ denim jackets at a cost of $$100,200.$ These jackets were damaged in the warehouse during storage. Management identified three alternatives for these jackets.

Jackets can be sold as scrap to a secondhand clothing shop for $$20,040.$

Jackets can be disassembled at a cost of $$6,680$ and sold to a recycler for $$40,080.$

Jackets can be reworked and turned into good jackets. The cost of reworking the jackets will be $$113,560,$ and the jackets can then be sold for $$150,300.$

Required:

$(1)$ Compute the income for each alternative.

$(2)$ Which alternative should be chosen?