Use Linear Programming

1. (50pts) Cozmo produces toy robots for various companies. Due to a large new order, Cozmo predicts that demand for its robot will be 12,500 units in the next quarter. This is a substantial increase relative to previous quarters and will challenge Cozmo's manufacturing capabilities. The robot consists of three key components: a housing unit, an engine unit, and a transistor unit. Cozmo is convinced that it will have to subcontract 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 robot is produced internally and the cost per unit for each component when purchased from an outside vendor: Cozmo's manufacturing facility has three departments: Assembly, Quality Control (QC), and Logistics. If produced internally, each component requires a certain amount of time (in hours/unit) in cach of these three departments. The following table shows these time requirements; the final row of the table shows the total number of hours available for robot production in the upeoming quarter. a) Formulate a Linear Program that can help Cozmo meet its predicted demand most efficiently. Clearly define 1) the decision variables, 2) the objective function, 3) the constraints. b) To avoid overreliance on outside vendors for an individual component, Cozmo 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, Cozmo wants to produce at least 65% of its engines internally. Adjust your formulation to incorporate this. 1. (50pts) Cozmo produces toy robots for various companies. Due to a large new order, Cozmo predicts that demand for its robot will be 12,500 units in the next quarter. This is a substantial increase relative to previous quarters and will challenge Cozmo's manufacturing capabilities. The robot consists of three key components: a housing unit, an engine unit, and a transistor unit. Cozmo is convinced that it will have to subcontract 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 robot is produced internally and the cost per unit for each component when purchased from an outside vendor: Cozmo's manufacturing facility has three departments: Assembly, Quality Control (QC), and Logistics. If produced internally, each component requires a certain amount of time (in hours/unit) in cach of these three departments. The following table shows these time requirements; the final row of the table shows the total number of hours available for robot production in the upeoming quarter. a) Formulate a Linear Program that can help Cozmo meet its predicted demand most efficiently. Clearly define 1) the decision variables, 2) the objective function, 3) the constraints. b) To avoid overreliance on outside vendors for an individual component, Cozmo 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, Cozmo wants to produce at least 65% of its engines internally. Adjust your formulation to incorporate this