Recall that in the network model formulation of this problem a node represents a year when the equipment was purchased. An arc from node i to node j indicates that the equipment purchased in year i can be replaced at the beginning of year j$.$ How could the following network model be modified to depict an equipment purchase in year $4$ and operating costs only through the remainder of the planning window?

Node $1$ connects to Nodes $2$ and $3$; Node $2$ connects to Nodes $3$ and $4$; Node $3$ connects to Nodes $4$ and $5$; and Node $4$ connects to Node $5.$ The coefficients for Nodes $1?5$ are: $-1,+0,+0,+0,$ and $+1,$ respectively.

$$

Group of answer choices

Add a dummy node, $6,$ so that arc $4-6$ represents just the operating costs.

Add a second arc $4-5$ to represent just the operating costs.

Modify the cost on arc $4-5$ to account for only operating costs.

Add a dummy node, $6,$ so that arc $4-5$ represents operating costs and $5-6$ represents a new equipment purchase.