$1.$ A crew that installs carpeting has the following output in each of the last $2$ weeks:

This week: $600$ feet of carpeting installed over $250$ man hours.

Last week: $500$ feet of carpeting installed over $220$ man hours.

Calculate the percentage change in productivity.

$2.$ Calculate the multifactor productivity for a catering company, using the following information:

In a week, the company produces $750$ meals at an average price of $$10$ per meal. The average cost for each meal is $$5.$ The catering company needed $3$ employees to work $40$ hours each at a rate of $$12$ per hour. The company has weekly overhead costs of $$200.$

$3.$ Today a worker processed $50$ records in $8$ hours. Yesterday, this same worker processed $48$ records in $7\mathrm{.}5$ hours.

a$.$ Calculate the productivity for each day

b$.$ Calculate the percentage change in productivity

c$.$ Does the change represent an increase or decrease in productivity?

d$.$ How do you know $($that this is in increase or a decrease$)?$