Problem $1(20\%)$:

The management of a company that produces custom computer components received a proposal about investing in advanced machinery to streamline its production processes. Currently, with the existing machinery, the company employs five technicians who assemble an average of $140$ components per hour in total. The labor cost is $$15$ per hour, and the machine cost is $$50$ per hour. According to the proposal, by implementing the new machinery, one technician can be reassigned to a different project. The machine cost will be increased by $$20$ per hour, but the output will be increased by six components per hour.

a$.$ Calculate labour productivity for the current and new machinery. Use components per hour as the measure of labour productivity. How much $($in percentage$)$ did labour productivity grow?

b$.$ Calculate the multi$-$factor productivity for the current and new machinery. Use components per dollar cost $($labour cost plus machine cost$)$ as the measure. How much $($in percentage$)$ did the multifactor productivity grow?