Trimble produces handheld GPS devices. Due to its popularity, Trimble believes that demand for its latest...

 

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Trimble produces handheld GPS devices. Due to its popularity, Trimble believes that demand for its latest GPS device will be 12,500 units in the next quarter. This is significantly larger than it was in previous quarters and may exhaust Trimble's production capacity. The handheld GPS device consists of three key components: a housing unit, an display unit, and a transistor unit. Trimble is convinced that it will have to outsource some of these units and purchase a number of these components from outside vendors because its internal capacity is limited. The table below shows both the production cost per unit for each component when the handheld GPS device is produced internally and the cost per unit for each component when purchased from an outside vendor: Component Housing Display Transistor Vendor Cost $19.50 $25 $12.10 Component Housing Display Transistor Capacity Trimble's manufacturing facility has three divisions: Assembly, Quality Control (QC), and Logistics. If produced in house, each component requires a certain amount of time (in hours/unit) in each of these three divisions. The following table shows the time needed per unit for each of the components and the final row of the table shows the total number of hours available for GPS device production in the upcoming quarter. Assembly 0.04 0.07 0.08 1650 Internal Cost $14.50 $23 $8.10 a) Define the decision variables. b) Define the objective function. QC 0.06 0.09 0.03 1650 Distribution 0.04 0.07 0.06 1650 Formulate a Linear Program that can help Trimble meet its predicted demand most efficiently. 2. c) Define the constraints. d) To avoid overreliance on outside vendors for an individual component, Trimble also wants to ensure that the number of transistors purchased from an outside vendor is somewhere between 40% and 60% of the total number of components subcontracted. Moreover, Trimble wants to produce at least 65% of its displays internally. Adjust your formulation to incorporate this. 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 с Model 1 3 5 2 Processing time in minutes GPS Device Model 3 4 Model 2 4 3 5 5 3 Model 4 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? Trimble produces handheld GPS devices. Due to its popularity, Trimble believes that demand for its latest GPS device will be 12,500 units in the next quarter. This is significantly larger than it was in previous quarters and may exhaust Trimble's production capacity. The handheld GPS device consists of three key components: a housing unit, an display unit, and a transistor unit. Trimble is convinced that it will have to outsource some of these units and purchase a number of these components from outside vendors because its internal capacity is limited. The table below shows both the production cost per unit for each component when the handheld GPS device is produced internally and the cost per unit for each component when purchased from an outside vendor: Component Housing Display Transistor Vendor Cost $19.50 $25 $12.10 Component Housing Display Transistor Capacity Trimble's manufacturing facility has three divisions: Assembly, Quality Control (QC), and Logistics. If produced in house, each component requires a certain amount of time (in hours/unit) in each of these three divisions. The following table shows the time needed per unit for each of the components and the final row of the table shows the total number of hours available for GPS device production in the upcoming quarter. Assembly 0.04 0.07 0.08 1650 Internal Cost $14.50 $23 $8.10 a) Define the decision variables. b) Define the objective function. QC 0.06 0.09 0.03 1650 Distribution 0.04 0.07 0.06 1650 Formulate a Linear Program that can help Trimble meet its predicted demand most efficiently. 2. c) Define the constraints. d) To avoid overreliance on outside vendors for an individual component, Trimble also wants to ensure that the number of transistors purchased from an outside vendor is somewhere between 40% and 60% of the total number of components subcontracted. Moreover, Trimble wants to produce at least 65% of its displays internally. Adjust your formulation to incorporate this. 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 с Model 1 3 5 2 Processing time in minutes GPS Device Model 3 4 Model 2 4 3 5 5 3 Model 4 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?

Answer rating: 100% (QA)

1 a Decision Variables Let X1 X2 and X3 represent the number of units of the housing display and transistor components to be produced internally respe... View the full answer