Chapter 5.2, Problem 51E

Water skis. A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The trick ski requires $6$ labor-hours for fabricating and $1$ labor-hours for finishing. The slalom ski requires $4$ labor-hours for fabricating and $1$ labor-hours for finishing. The maximum labor-hours available per day for fabricating and finishing are $108$ and $24$, respectively. If $x$ is the number of trick skis and $y$ is the number of slalom skis produced per day, write a system of linear inequalities that indicates appropriate restraints on $x$ and $y$. Find the set of feasible solutions graphically for the number of each type of ski that can be produced.