Refer to Problem 51. The company makes a profit of $50 on each trick ski and a profit of $60 on each slalom ski.

(A) If the company makes 10 trick skis and 10 slalom skis per day, the daily profit will be $1,100. Are there other production schedules that will result in a daily profit of $1,100? How are these schedules related to the graph of the line 50x + 60y = 1,100?

(B) Find a production schedule that will produce a daily profit greater than $1,100 and repeat part (A) for this schedule.

(C) Discuss methods for using lines like those in parts (A) and (B) to find the largest possible daily profit.

Data from Problem 51

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-hour for finishing. The slalom ski requires 4 labor-hours for fabricating and 1 labor-hour 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.