Chapter 5.3, Problem 1ED

Refer to the feasible region $S$ shown in Figure 3.

(A) Let $P=x+y$. Graph the constant-profit lines through the points $\left(5,5\right)$ and $\left(10,10\right)$. Place a straightedge along the line with the smaller profit and slide it in the direction of increasing profit, without changing its slope. What is the maximum value of $P$ ? Where does this maximum value occur?

(B) Repeat part (A) for $P=x+10y$.

(C) Repeat part (A) for $P=10x+y$.