2. Germanium is an important element for producing transistors for semi-conductors. Unfor- tunately, the process for obtaining germanium results is highly variable in the production quality. An hour of labour results in the following amounts of Germanium. Table 1: Units of Germanium Produced per Production Hour Grade 0 (Defective) Grade 1 Grade 2 Cost per Hour Germanium Produced: 2 5 3 $65 Each unit of grade 1 and grade 2 germanium sell for $10 and $14 respectively. Defective germanium has no sell-value. Fortunately, both defective and grade 1 germanium can be refined into higher quality germanium: An hour of refining defective germanium converts 8 units of defective germanium into 4 units of grade 1 germanium 4 units of grade 2 germanium. An hour of this process costs $50 An hour of refining grade 1 germanium converts 10 units of grade 1 germanium into 10 units of grade 2 germanium. An hour of this process costs $30. In total, there are 200 labour hours available for the 3 processes. Formulate a linear program to determine how to optimally produce and refine germanium. Hint: Think carefully about your decision variables. Note 1: While you are allowed to, you are not required to parameterize this