What point maximizes the objective function

Question

P = 4x + 3y for the constraints below. What is the maximum value?

Constraints:

x>=0
y>=0
y<=1/3x-4
6>=y

Answer 1

Graph the inequalities given by the set of constraints. Find points where the boundary lines intersect to form a polygon. Substitute the coordinates of each point into the objective function and find the one that results in the largest value.