$[10]$ Consider a network of cities connected by roads, where each road has a specific travel

cost$.$ The cities are labeled A$,$ B$,$ C$,$ D$,$ and E$.$ The travel costs between the cities are as follows:

A to B is $$4,$A to C is $$2,$ B to D is $$5,$C to D is $$8,$C to E is $$10,$ and D to E is $$3.$ Your task is

to find the shortest path from city A to city E that minimizes the total travel cost. These data are

provided in the accompanying Excel workbook

$($a$)[4]$ Formulate this shortest path problem as a linear program. Clearly define your decision

variables, objective function, and constraints.

$($b$)[4]($Excel$)$ Solve this linear program in the Excel workbook. What is the minimum total cost

of travel from A to E $?$ Write down the answer here; save the answer report and the sensitivity

report in Excel.

$($c$)[2]$ If the travel cost from C to D is changed to $$5.$ Will the optimal solution change? If so$,$

what will be the new optimal solution and optimal value? Explain $($to the best you can$)$ how it will

change. Answer this question by reading from the sensitivity report without resolving the linear

program.

NOTE: PLEASE MAKE IT CLEAR ON THE ANSWERS FOR A$,$B$,$C PLEASE SHOW YOUR WORK $!$