A manufacturer produces two types of DVD player: Vista and Xtreme. During production, the players require the use of two machines, A and B. The number of hours needed on both machines are indicated in the following table: Vista Xtreme Machine A 1 hour 3 hours Machine B 2 hours 2 hours If each machines can be used 24 hours a day, and the profits on the Vista and Xtreme models are $50 and $80, respectively, how many of each type of player should be made per day to obtain maximum profit? What is the maximum profit? Make sure to label the variables using a complete sentence, write the system of inequalities and objective function, graph the feasible region, determine the corner points, plug in all of the corner points into the objective function, and write your answer as a complete sentence.