Problem $3.$ Shortest Path Problem $(3$ pts$)$ USE EXCEL TO SOLVE

You are driving from O to T $.$ You would like to minimize the total distance by taking any possible nodes that enable you to start from O and terminate at T $.$

Hint $1$: A shortest path problem is a simplified "minimum cost" problem. The "costs" associated with each arc are the distances, which need to be minimized.

Hint $2$: A shortest path problem is always a balanced network problem, where "supply" is equal to "demand." You are the "supply" as well as the "demand." How many entities are transported from O to T $?$ This is the key to solving this problem.

$($a$)$ Write the complete LP formulation in standard algebraic form. Clearly specify the objective function, all arc capacity constraints, and all node flow constraints mathematically!

$($b$)$ Using Solver, compute the distance corresponding to the shortest path. Trace the path explicitly. Use the "SUMIF" function as demonstrated in class. You will be penalized if you don't use the "SUMIF" function.