$12-23.In$ each $of$ the following cases, develop the network, and find the optimal solution for

the model $in$ Example $12\mathrm{.}3-3$:

$(a)$ The machine $is2$ years old $at$ the start $of$ year $1.$

$(b)$ The machine $is1$ year old $at$ the start $of$ year $1.$

$(c)$ The machine $is$ bought new $at$ the start $of$ year $1.$