The feasible region shown below is bounded by lines – x + 3y = 3, x + y = 4, and y = 0

feasible-region
coordinates-corne

#1

The feasible region shown below is bounded by lines – x + 3y = 3, x + y = 4, and y = 0.

Find the coordinates of corner point A. Show work.

Answer:

Solve the two equations below to determine the coordinates of corner point A.

-x+3y =3 … (1)
x+y =4 … (2)

Express equation (2) in terms of y.
y = 4-x …(3)

Substitute 4-x for y in equation (1).
-x+3(4-x)=3
-x+12-3x=3
4x=9
x=9/4

Substitute 9/4 for x in equation (3).
y=4 - (9/4)
y=(16-9)/4
y=7/4

Therefore the coordinates of corner point A is (9/4 , 7/4).