Problem $1$

Rototech Corp. supplies motors for all washing machines manufactured by Launders Inc.

The motors are produced in Rototech$$s facilities located in New York City, Fort Worth, and

San Diego. Rototech$$s production capacities are as follows:

New York City $60,000$

Fort Worth $40,000$

San Diego $60,000$

Launders Inc. manufactures the washers at five locations around the country. Based on the

manufacturing plans over the next $12$ months, the following table provides the number of motors

required at each Launders Inc. manufacturing location:

Boulder $20,000$

Minneapolis $30,000$

Gary $30,000$

Memphis $50,000$

Macon $20,000$

Shipments will be made in lots of $1,000$ motors from Rototech to Launders. Due to varying

production and distribution costs, Rototech$$s profits depend on where the motors are produced

and where they are shipped. Based on estimates from Rototech$$s Accounting Department, the

following table provides the profit in dollars per unit.

Shipped To

Produced at Boulder Minneapolis Gary Memphis Macon

New York $$10$ $$15$ $$16$ $$14$ $$17$

Fort Worth $$15$ $$16$ $$18$ $$19$ $$18$

San Diego $$16$ $$14$ $$12$ $$15$ $$12$

Given profit maximization as a criterion, use the Transportation Method of Linear

Programming to determine the optimum ship quantity from each Rototech location to

each Launders Inc. location. Include the following items in your response:

$($a$)$ Submit your Excel file Solver add$-$on

Demonstrate your understanding of the Solver results by answering the following questions:

$($b$)$ Based on your solution, how many motors should be shipped from Fort Worth to Memphis?

$($c$)$ Based on your solution, report how much additional production capacity is still available at each of Rototech$$s production plant