Question $-1.(6$ points$)$

Falcon Financial is a health insurance company considering an investment in a new software platform that promises faster handling of policy applications. Currently, a team of $12$ employees works $7$ hours per day, with a labor cost of $\backslash (\backslash$$ $30\backslash )$ per hour per person. In addition to labor costs, the facility incurs $\backslash$$$2,500$ per day in miscellaneous expenses related to processing applications. On average, the company processes $200$ applications per day.

With the new software system, Falcon Financial will be able to process $270$ applications per day. The number of staff members, hourly labor cost, and working hours will remain unchanged, but daily miscellaneous expenses will increase to $\backslash (\backslash$$ $3,200\backslash ).$

Calculate the expected change in multifactor productivity for invest in the new software platform by answering the questions below.

NOTE $1$: SHOW ALL YOUR WORK. USE $4$ DECIMAL PLACES IN YOUR CALCULATIONS.

NOTE $2$: YOU SHOULD PROVIDE AND EXPLAIN ALL STEPS ON YOUR WORKSHEET.

a$)(1$ point$)$ What is $($are$)$ the input$($s$)$ that would be used to calculate productivity at Falcon Financial?

b$)(1$ point$)$ What is $($are$)$ the output$($s$)$ that would be used to calculate productivity at Falcon Financial?

c$)(1$ point$)$ Calculate the daily labor productivity using the cost of labor.

d$)(1$ point$)$ How can you compute the daily multi$-$factor productivity for Falcon Financial? $($Your answer should be in the form of a formula without any numbers or calculations.$)$

e$)(2$ points$)$ What is the expected percentage change in the daily multifactor productivity at Falcon Financial if the company invests in the new computer system?

NOTE: Use $4$ decimal points in all your calculations. MAKE SURE YOU CLEARLY LABEL AND HIGHLIGHT YOUR ANSWERS TO EACH QUESTION.