• A computer-typed Word file that contains the solution to the problems in this assignment. For equations, use Microsoft Words equation editor. Use figures as needed. This Word file must include the LP formulation required in Problem 1a (including definition of variables objective function, constraints, and final model, as seen in class) and the numerical solutions and interpretations of all other problems or subproblems in this assignment.
• An Excel file that contains three tabs (Problem 1b, Problem 2, Problem 3) with Solvers solution to these problems. Note that it is imperative that Excel file and Solver are set up so the grader can run the model with Solver and obtain a solution immediately.
• In both files, the names of all the group members must appear.

For general guidelines on how to present your assignments, refer to the courses syllabus.

For policy on late submissions, refer to the courses syllabus.

Problem 1 (35 pt)

Bowman & Kinkins (B&K) is a hi-fi speaker manufacturer. They proudly engineer and manufacture their speakers in the United Kingdom. To celebrate their 75-year anniversary, they will release a Limited Edition of their most well-known speakers from the acclaimed 6000 Series, the floorstanding speaker B&K 6003.

B&K has three manufacturing plants in the UK (Manchester, Edinburgh, Southampton) that will be in charge of producing a first batch of these hi-fi limited-edition speakers. Their production will be sent to B&Ks distribution centers in other continents. More concisely, these distribution centers are located in Santiago de Chile (Chile), Atlanta (USA), Frankfurt (Germany), and Shanghai (China). The cost of producing these speakers varies with the location they are produced at. Likewise, transporting them to the companys distribution centers has a variable transportation cost that depends on the route. Production costs and capacities for the next month are given in Table 1. The amount that needs to be put in inventory in each distribution center is shown in Table 2. The transportation costs (in USD/speaker) are given in Table 3

in each distribution center is shown in Table 2. The transportation costs (in USD/speaker) are given in Table 3. Production cost (per speaker) Capacity (in speakers) Manchester $100 100 Edinburgh $75 100 Southampton $90 80 Table 1 Santiago Atlanta Frankfurt Shanghai Demand (tons) 80 70 40 60 Table 2 Shipping cost (per speaker) Santiago Atlanta Frankfurt Shanghai Manchester 11 8 4 15 Edinburgh 12 4 12 Southampton 10 8 13 9 4 Table 3 a) (18pt) Problems in B&K's procurement of raw materials has resulted in shortage of their production capacity. Consequently, their new production capacities are shown in Table 4. Formulate an LP model that can at least tell B&K how to better distribute the production they can come up with. b) (17pt) Solve this model with Excel and interpret its solution. Production cost (per speaker) Capacity (in speakers) Manchester $100 45 Edinburgh $75 70 Southampton $90 55 Table 4 2 Problem 2 (30 pt) Consider the network below: 6 4 1 2. 5 6 If the numbers by the edges indicate distance, use Excel's Solver to find the shortest path between nodes 1 and 7. Note that arcs can be traversed in both directions. Clearly indicate this path. Problem 3 (35 pt) Consider the network below: 4 G 2 6 3 3 4 3 1 7 5 1 6 B E H 8 2 10 3 1 I If the numbers by the edges indicate capacity, use Excel's Solver to find the maximum flow that can be sent between nodes s and t. Clearly indicate the value of this flow and the way it would traverse the network. 3 in each distribution center is shown in Table 2. The transportation costs (in USD/speaker) are given in Table 3. Production cost (per speaker) Capacity (in speakers) Manchester $100 100 Edinburgh $75 100 Southampton $90 80 Table 1 Santiago Atlanta Frankfurt Shanghai Demand (tons) 80 70 40 60 Table 2 Shipping cost (per speaker) Santiago Atlanta Frankfurt Shanghai Manchester 11 8 4 15 Edinburgh 12 4 12 Southampton 10 8 13 9 4 Table 3 a) (18pt) Problems in B&K's procurement of raw materials has resulted in shortage of their production capacity. Consequently, their new production capacities are shown in Table 4. Formulate an LP model that can at least tell B&K how to better distribute the production they can come up with. b) (17pt) Solve this model with Excel and interpret its solution. Production cost (per speaker) Capacity (in speakers) Manchester $100 45 Edinburgh $75 70 Southampton $90 55 Table 4 2 Problem 2 (30 pt) Consider the network below: 6 4 1 2. 5 6 If the numbers by the edges indicate distance, use Excel's Solver to find the shortest path between nodes 1 and 7. Note that arcs can be traversed in both directions. Clearly indicate this path. Problem 3 (35 pt) Consider the network below: 4 G 2 6 3 3 4 3 1 7 5 1 6 B E H 8 2 10 3 1 I If the numbers by the edges indicate capacity, use Excel's Solver to find the maximum flow that can be sent between nodes s and t. Clearly indicate the value of this flow and the way it would traverse the network. 3