The vertices of a feasible region are (0,3) (4,6) (0,0) and (7,3). What is the maximum value of the function P = 4x + 3y?

Question

The vertices of a feasible region are (0,3) (4,6) (0,0) and (7,3). What is the maximum value of the function P = 4x + 3y?

Answer 1

This is a linear programming problem. In linear programming, the maximum and minimum values of a function occur at the vertices of the feasible region. Since we're given the feasible region's vertices in this problem, all we have to do is plug each of the coordinate points into the function for P, and the maximum will be found:

(0,3): P = 3*0 + 3*3 = 9

(4,6): P = 4*4 + 3*6 = 34

(0,0): P = 0*0 + 0*0 = 0

(7,3): P = 4*7 + 3*3 = 37

Therefore, the maximum value of P in the feasible region is 37, which occurs at the point (7,3).