Chapter 5.2, Problem 46E

Furniture. Refer to Problem 52. The company makes a profit of $\text{\$}50$ on each table and a profit of $\text{\$}15$ on each chair.

(A) If the company makes $20$ tables and $20$ chairs per day, the daily profit will be $\text{\$}1,300$. Are there other production schedules that will result in a daily profit of $\text{\$}1,300$ ? How are these schedules related to the graph of the line $50x+15y=1,300$ ?

(B) Find a production schedule that will produce a daily profit greater than $\text{\$}1,300$ 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.