$9-37$

The numbers in the network below represent thousands of gallons per hour as they flow through a chemical processing plant. Two terminals in the chemical processing plant, represented by nodes $6$ and $7,$ have had problems recently, and repairs on these are being considered. However, these repairs would require that these terminals $($nodes$)$ be shut down for a significant amount of time, and no material could flow into or out of these nodes until the repairs are finished. What impact would closing these nodes have on the capacity of the network? Answer in detail with this format:

$1.$ Definition of the decision variables including the units specified.

$2.$ The objective function including its social, economic or physical meaning, and the units specified.

$3.$ All the constraints in mathematical equation or inequality, and the social, economic or physical meaning for each of them, and the units specified. $($Include Calculations and Verification of Constraints.$)$

$4.$ Optimal Solution and its interpretation of the optimal decision and conclusion in the context of the original problem.