Question

Maximise Z = 5x + 3y 

subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0,y ≥ 0

Answer 1

3x + 5y ≤ 15

x	0	5
y	3	0

0 + 0 <15 

true, toward 0

5x +2y = 10

x	2	0
y	0	5

ABCD is the solution region 

At A(0,3) ,Z = 3 x 3 = 9

Comments

At C(2,0), Z = 5x2 = 10
But....
At the point (20/19, 45/19), Z = 12.355
You must check ALL of the points to check for maximum value!