Question $4(25$ Points$)$

"Evolution Sails, a new sail maker in the industry, is trying to figure out where to place their regional Sail Lofts $($Customer Service, small repair, and Distribution Centers$).$ The company has narrowed down their options to the different options that can be found in cells C$2$:M$2$ on the worksheet Question $4$ Model. They would like to place their Sail Lofts in locations that allow the company to minimize the distance between the Sail Lofts and their customers, which can be found in cells B$3$:B$50$ on the worksheet Question $4$ Model.

Each Evolution Sail Loft has the capacity to serve up to eight customers. Identify where to place the Sail Lofts, which customers each Sail Loft services, and the total distance between the Sail Lofts and their customers. Please note that Evolution Sails wants to serve all customers in order to continue to build their reputation in the industry. They also want to provide speedy service and thus want to operate at least seven lofts. In order to limit fixed cost risks they don't want to open more than nine lofts.

All of the distance data are provided on the worksheet Question $4$ Model. Please note that due to the large number of decision variables you must use OpenSolver to solve this problem."

a$)(5$ points$)$ Identify, using binary variables $(0,1),$ in which cities to place the Sail Lofts $(1=$Yes$).$ Make sure to use a reference to your solution. Do NOT just enter a number.

Sail Loft $1$ Sail Loft $2$ Sail Loft $3$ Sail Loft $4$ Sail Loft $5$ Sail Loft $6$ Sail Loft $7$ Sail Loft $8$ Sail Loft $9$ Sail Loft $10$ Sail Loft $11$

b$)(15$ points$)$ Identify, using binary variables $(0,1),$ which customers wille be servered by which Sail Lofts service. Make sure to use a reference to your solution. Do NOT just enter a number.

Sail Loft $1$ Sail Loft $2$ Sail Loft $3$ Sail Loft $4$ Sail Loft $5$ Sail Loft $6$ Sail Loft $7$ Sail Loft $8$ Sail Loft $9$ Sail Loft $10$ Sail Loft $11$

Duluth YC $1$

Wayzata YC

Chicago YC $1$

Columbia YC $1$

San Francisco YC

Los Angeles YC $1$

San Diego YC $1$

Newport YC

Annapolis YC

Charleston YC

Miami YC

Atlanta YC

Avalon YC

Bay City YC

Bayfield YC

Camden YC

Duck Island YC

Edgewater YC

Fairview YC

Genesee YC

Buffalo YC

Hampton YC

Bayview YC

Juneau YC

Long Beach YC

Marblehead YC

Navy YC

Palm Beach YC

Hamburg YC

Kiel YC

Flensburg YC

Munich YC

Sidney YC

Hobart YC

Melbourne YC

Adelaide YC

Portsmouth YC

Southhampton YC

Brighton Beach YC

Marsaille YC

La Rochelle YC

Lisbon YC

Barcelona YC

Copenhagen YC

Aarhus YC

Helsingborg YC

Cannes YC

Naples YC

c$)(4$ points$)$ What is the minimum distance according to this plan? Make sure to use a reference to your solution. Do NOT just enter a number.