Which of these points does not satisfy the constraints?

Question

Which of these points does not satisfy the constraints?
6x + 8y <= 48, x + y <= 7, x >= 0, y >= 0


a) (1,6)
b) (4,3)
c) (6,1)
d) (1,4)

Answer 1

check them out one by one.
Each point is given in the form (x, y) and you use the values for the appropriate variable in each constraint.

For example,
a) (1, 6)
x = 1
y = 6

then
6x + 8y = 6 + 48 = 54
which is greater than 48 (not OK)
x + y = 1 + 6 = 7
which is equal to 7 (OK)
x = 1 which is more than 0
y = 6 which is more than 0

With a quick glance, you can tell that all x are greater than 0, all y are greater than 0 and that x+y is never greater than 7.

Therefore, you only need to check the first contraint.