Searching for ways to cut costs and increase profit, one of the industrial engineers at Home Comfort Furniture Manufacturers, Inc.

determined that the equivalent annual worth of an existing machine over its remaining useful life of $2$ years is $$-68,000$ per year. The

IE also determined that used machines like the one currently in use are not available any longer, but the defender can be replaced

with a challenger that is more advanced. It will have an AW of $$-80,050$ if it is kept for $2$ years or less, $$-73,575$ if it is kept between $3$

and $4$ years, and $$-65,000$ if it is kept for $5$ to $10$ years. If the company uses a specified $3-$year planning horizon and an interest rate of

$10\%$ per year.

a$)$ Determine when the company should replace the machine.

b$)$ Determine the AW for the next $3$ years.

a$)$ The company should Keep the machine for $2$ years and then replace with the challenger $v.$

b$)$ The AW for the next $3$ years is $