$**$Please provide detailed solution with formulas and calculations please. No table or excel sheet please.$**$

A medium size assembly plant is considering re$-$designing one of its assembly stations. The station is currently operated by $2$ assembly labors. Due to the complexity of the task, fully automating the assembly station is not achievable. However, it is possible to replace one of the labors with a collaborative robot that can work safely along with the other labor. The plant has a MARR $($Minimum Acceptable Rate of Return$)$ of $7\backslash \%.$ The lable below summarizes the cost for one labor and the cost for one collaborative robot. Use the information in the table to answer the following questions.

a$)$ If the assembly operation is to be re$-$programmed every year, is it an economic decision to replace one labor with a collaborative robot? $($Use Present Worth$)$

$(6$ Marks$)$

b$)$ If the assembly operation is to be re$-$programmed every $2$ years, is it an economic decision to replace one labor with a collaborative robot? $($Use Present Worth$)$

$(7$ Marks$)$

c$)$ Redo question a$)$ using Annual Worth instead of Present Worth

$(7$ Marks$)$

d$)$ Do both methods $($Present Worth and Annual Worth$)$ always lead to the same decision?

$(5$ Marks$)$