Suppose a shop needs to have a certain machine over the next five$-$year period. Each new machine costs Rs$.1,000.$ The cost of maintaining the machine during its $\text{'}i\text{'}$ th year of operation is as follows: $m1=$ Rs$.60,m2=$ Rs$.80$ and $m3=$ Rs$.120.$ A machine may be kept up to three years before being traded in$.$ The trade in value after i years is $S1=$ Rs$.800,$ s$2=$ Rs$.600$ and $s3=$ Rs$.500.$ How can the shop minimize costs over the five$-$year period? Give the stages in arriving the answers.