Chapter 5.2, Problem 42E

Problems 49 and 50 introduce an algebraic process for finding the corner points of a solution region without drawing a graph. We will discuss this process later in this chapter.

Consider the following system of inequalities and corresponding boundary lines:

$\begin{array}{c}2x+y\le 16\text{ 2}x+y=16\\ 2x+3y\le 362x+3y=36\\ x\ge 0x=0\\ y\ge 0y=0\end{array}$

(A) Use algebraic methods to find the intersection points (if any exist) for each possible pair of boundary lines.

(There are six different possible pairs)

(B) Test each intersection point in all four inequalities to determine which are corner points.