Dr$.$ Chiang is invited to develop a network plan. Unfortunately, he is occupied with his travel plan for his daughter to compete in the US Kid World Champion Tournament. Dr$.$ Chiang heard that you are a well$-$trained logistics professional. He$,$ thus, looks for your help to have this plan complete within the given time. Below is the information about the plan. Dr$.$ Chiang also shared with you part of his ongoing work $($Working sheet.xlsx$)$ to help you save time working out the plan.

Darin from Wisconsin is root beer crazy. His family recipe uses a special hop making his beer attractive to the regional market. Assume Darin lives in Node $1$ and his major client is at Node $10,$ as shown in the network below. The number on each arc shows the number of hours needed to travel between every two nodes.

Please provide your complete model formulation work $($define decision variables, create an objective function, and formulate constraint functions$)$ on Excel and turn in this Excel file for grading purposes. NOTE, if you fail to turn in the Excel file, you will have a significant grade loss..

Please find the shortest route from Node $1$ to Node $10$ using the amount of time for travel. $($Please show your answer in a series of numbers, such as $15910,$ meaning moving from $1$ to $5$ to $9$ to $10).$

Please find the time spent on the shortest route from Node $1$ to Node $10.$

Using the information about the speed limit on the road, try to build another travel plan. $($Please show your answer in a series of numbers, such as $15910,$ meaning moving from $1$ to $5$ to $9$ to $10)$

Travel Time $($Hours$)$ To

$12345678910$

$18131510$

From $2515$

$305$

$4243$

$512$

$6425$

$724$

$857$

$95$

$10$

Speed Limit $($miles per hour$)$

To

$12345678910$

$160402535$

From $25530$

$350$

$4804035$

$535$

$6606555$

$710080$

$87545$

$980$

$10$