Algebra 2 question about system of equations and inequalities

Question

Find the coordinates of the ordered pair where the maximum value occurs

for the equation P=4x+6y+22, given these constraints:

−4x + y ≥ 2

x ≥ − 3

y ≤ 22

Answer 1

This is a Linear Programming problem. Solve it as follows.

1. Graph the three given inequalities. They define a triangular shaped area called the feasible region. All of the solutions to P lie in the feasible region.
2. Identify the three vertices of the triangular feasible region. Label them as A, B, and C and write down their (x,y) coordinates. The maximum value of P will occur at one of these vertices (A, B, or C).
3. Plug in the (x,y) coordinates of A into equation P and write down the value of P. Do the same for points B and C.
4. The largest value of P from points A, B, and C is the maximum value of P. The (x,y) coordinates of the point (A, B, or C) that yielded the maximum value of P are ordered pair asked for in the problem

Answer 2

P = 34

x = -3

y = 4