2. (50pts) Trimble produces handheld GPS devices. Before they shipped, these GPS devices undergo a quick...

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2. (50pts) Trimble produces handheld GPS devices. Before they shipped, these GPS devices undergo a quick test on one of three machines in Trimble's quality control department. Trimble has five types of GPS devices, and any of the machines can be used to test any of the GPS devices. However, the time required for testing on each machine depends on the GPS device, as shown in the following table: Machine A B C Model 1 3 5 2 Processing time in minutes GPS Device Model 3 4 5 3 Model 2 4 3 5 Model 4 5 4 3 Model 5 3 5 4 Today, Trimble's QC department has 80 Model 1 devices, 75 Model 2 devices, 80 Model 3 devices, 120 Model 4 devices, and 60 Model 5 devices that need to be checked. Each machine can be used for a maximum of 8 hours per day, and Trimble wants to determine how many of each GPS device type to test on each machine so as to minimize the total time used for testing (leaving as much time as possible for other tasks the department has to perform). a) Formulate a Linear Programming model for this problem. Clearly define the decision variables, the objective function, and the constraints. b) Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? c) Suppose now that Trimble's QC department wants to make sure that each machine is used approximately the same amount of time. How will this impact the optimal solution? 2. (50pts) Trimble produces handheld GPS devices. Before they shipped, these GPS devices undergo a quick test on one of three machines in Trimble's quality control department. Trimble has five types of GPS devices, and any of the machines can be used to test any of the GPS devices. However, the time required for testing on each machine depends on the GPS device, as shown in the following table: Machine A B C Model 1 3 5 2 Processing time in minutes GPS Device Model 3 4 5 3 Model 2 4 3 5 Model 4 5 4 3 Model 5 3 5 4 Today, Trimble's QC department has 80 Model 1 devices, 75 Model 2 devices, 80 Model 3 devices, 120 Model 4 devices, and 60 Model 5 devices that need to be checked. Each machine can be used for a maximum of 8 hours per day, and Trimble wants to determine how many of each GPS device type to test on each machine so as to minimize the total time used for testing (leaving as much time as possible for other tasks the department has to perform). a) Formulate a Linear Programming model for this problem. Clearly define the decision variables, the objective function, and the constraints. b) Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? c) Suppose now that Trimble's QC department wants to make sure that each machine is used approximately the same amount of time. How will this impact the optimal solution?