$4.$ Sharon has applied to the Navy. She plans to play racquetball and cycle to get into shape for the fitness test. Sharon wants to spend no more than $12$ hours exercising a week and wants to burn a maximum of $7000$ calories. She has calculated that she will burn $700$ calories per hour playing racquetball and $350$ calories per hour bicycling. $(8$ marks$)$ a$)$ To describe this scenario, what quantities should $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ represent? function for this scenario. How much time should she spend on each activity in order to minimize costs? c$)$ Graph the system of inequalities, mark the points of intersection of all lines and shade the solutinn mananan a$)$ now mucn time snould she spend on each activity if she just wants to maximize her calorie burn?