4. A project manager at Intellix Corp. must oversee the development of a new traffic management system for the City of Paris. The team will consist of software engineers and hardware engineers. Although some tasks can be performed by either type of engineer, the manager knows from experience that at least 80 software engineers will be required for an efficient project, and at least 50 hardware engineers. In addition, the workload will require at least 200 engineers total on the team. The salary of a software engineer is $120,000 and for a hardware engineer it is $80,000. The manager wants to hire the right combination of engineers to minimize the total salary required while still meeting the requirements for numbers of engineers described above. a. Formulate this problem as a linear program. b. To the right is a graph of the constraints and the feasible space of this formulation. Draw one or more trial objective function lines and circle to optimal solution point. c. In the solution, which constraints have slack and which have surplus and which have neither? d. Which constraints are binding and which are nonbinding? e. How many software engineers and how many hardware engineers does this solution appear to recommend? f. For any constraint you identified in question (c) as having slack or surplus, how much slack or surplus does it appear to have