A firm utilizes a strategy of capital rationing, which is currently limited at $$375,000$ and is considering the following two projects:

Project A has a cost of $$335,000$ and the following cash flows: year $1$:$$140,000$; year $2$:$$150,000$; and year $3$:$$100,000.$

Project B has a cost of $$365,000$ and the following cash flows: year $1$$$220,000$; year $2$$$110,000$; and year $3$$$150,000.$

Using a $6\%$ cost of capital, which project should the firm choose?

can you show your work step by step please