#$1.$ A Company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used $6$ workers, who produced an average of $80$ carts per hour. Workers receive $$10$ per hour, and machine coast was $$43$ per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $$13$ per hour while output increased by four carts per hour.

a$)$ Compute the multifactor productivity $($MFP$)($labor plus equipment$)$ under the Prior to buying the new equipment. The MFP $($carts$/$$$)=------------($round to $4$ decimal places$).$

b$)$ Compute the productivity changes between the Prior to and after buying the new equipment. The productivity growth $=------($round to $2$ decimal places$)$

#$2.$ Compute the multifactor productivity measure for an $8$ hour day in which the usable output was $630$ units, produced by $5$ workers who used $905$ pounds of materials. Workers have an hourly wage of $21$ and material cost is $1\mathrm{.}9$ per pound. Overhead is $1\mathrm{.}6$ times labor cost.

The multifactor productivity $($units$/$$$)=----------($round to $4$ decimal places$)$

#$3.$A health club has $3$ employees who work on lead generation. Each employee works $25$ hours a week, and is paid $$23$ an hour. Each employee identifies an average of $220$ possible leads a week from a list of $8,000$ names. Approximately $10$ percent of the leads become members and pay a one$-$time fee of $$115.$ Material costs are $$195$ per week, and overhead costs are $$1,205$ per week. Calculate the multifactor productivity for this operation in fees generated per dollar of input.

The multifactor productivity for this operation in fees generated per dollar of input $=-------($round to $4$ decimal places$)$