A health club has $2$ employees who work on lead generation. Each employee contacts leads $20$ hours a week and is paid $$22$ per hour.

Each employee contacts an average of $180$ leads a week. Approximately $11\%$ of the leads become members and pay a onetime fee of $$100.$

Material costs are $$190$ per week, and overhead costs are $$1,100$ per week.

a$.$ Calculate the multifactor productivity for this operation in fees generated per dollar of input. $($Do not round intermediate calculations. Round your final answer to $2$ decimal places.$)$

b$.$ The club's owner is considering whether to purchase a new software program that will allow each employees to contact $20$ more leads per week. Material costs will increase by $$160$ per week. Overhead costs will remain the same.

Calculate the new multifactor productivity if the owner purchases the software. $($Do not round intermediate calculations. Round your final answer to $2$ decimal places.$)$

c$.$ How would purchasing the software affect productivity? $($Enter the change in productivity as a percentage rounded to one decimal.$)$