$1-13.$ Consider this situation faced by a soon$-$to$-$graduate engineering student from a top university. Farah has been offered a job at a successful company. At the same time, she has been offered a scholarship to complete a two$-$year master's program in her specialization of choice. She is exhausted from studying for exams and is tempted to take up the job. However, if she takes the job, she loses the scholarship, which she may never win again. If she takes the scholarship, she may not get a job after two years.

a$.$ Develop at least two formulations for Farah's problem.

b$.$ Identify feasible solutions for each problem formulation in Part $($a$).$ Be creative.