Question $2$:

In $1862,$ during the second year of the Civil War, General Thomas J$.$ "Stonewall" Jackson fought a brilliant military campaign in the Shenandoah Valley in Virginia. One of his victories was at the Battle of MCDowell. Using the following figure and your imagilation, determine the shortest path and how long it will take $($in days$)$ for General Jackson to move his army from Winchester to McDowell to fight the battle. The network is shown in the figure below, and copy paste friendly set of branches are collected in the table below.

a$)$ Formulate a binary programming model to determine the shortest path and how long it will take $($in days$)$ for General Jackson to move his army from Winchester to McDowell to fight the battle. $($i$.$e$.,$ Write down a mathematical model$)($Note that you still need to provide the mathematical model in Part a if you choose to apply the algorithm in Part b$)(10$ pts$)$

b$)$ Solve the binary programming model by using Excel. $(40$ pts$)$