Marginal cost$-$benefit analysis and the goal of the firm Ken Allen, capital budgeting analyst for Bally Gears, Inc., has been asked to evaluate a proposal. The manager of the automotive division believes that replacing the robotics used on the heavy truck gear line will produce total benefits of $$531,000($in today's dollars$)$ over the next $5$ years. The existing robotics would produce benefits of $$421,000($also in today's dollars$)$ over that same time period. An initial cash investment of $$212,400$ would be required to install the new equipment. The manager estimates that the existing robotics can be sold for $$72,000.$ Show how Ken will apply marginal cost$-$benefit analysis techniques to determine the following:

a$.$ The marginal benefits of the proposed new robotics.

b$.$ The marginal cost of the proposed new robotics.

c$.$ The net benefit of the proposed new robotics.

d$.$ What should Ken recommend that the company do$?$ Why?

e$.$ What factors besides the costs and benefits should be considered before the final decision is made?

a$.$ The marginal $($added$)$ benefits of the proposed new robotics is $ $($Round to the nearest dollar.$)$