Arun and Kasuni operate a small special mail processing business for the USPS on a contract. The following table shows their mail processing information. They want to evaluate the productivity of their mail processing centers. The centers differ in the degree of automation, the type of work that can be performed, and the skill of the workers. It also differs in the number of workers processing mail daily and also the number of hours each worker works per day processing mail.

Center $123$

Pieces processed per day $1,5002,0003,000$

Number of workers per day $1052$

Hours worked per worker per day $458$

Hourly wage rate $$12\mathrm{.}00$ $$13\mathrm{.}00$ $$15\mathrm{.}00$

Fixed cost per center or overhead cost NA NA

a$)$ Calculate the labor hours productivity for Center $1$ and $2$

b$)$ A new processing machine is available for Center $1$ that will increase the output to $1,900($Center One new output$)$ pieces a day, but this will increase an additional cost, which will be an overhead cost of $$175\mathrm{.}00$ per day. Merrifield will only install the new processing machine if it increases the multifactor productivity of Center $1$ by at least $10\%.$ Should Merrifield install the new processing machine? Justify your answer. Also, what is the percentage change in the multifactor productivity performance?

Before and after comparison formula

New productivity $$ old productivity$/$ old productivity $*100$