Consider the following linear system of inequalities:

Question

Consider the following linear system of inequalities:

x+y ≤ 30, 2x-y≥-10, x ≥0, y≥0

Draw the feasible set and label the axes, lines and all intercepts. Put F.S. where the feasible set should be in the drawing. Find and list the corner points.

Answer 1

x + y ≤ 30 Let this one be (1)

2x - y ≥ -10 and this one (2)

Solve this system of inequalities as follows:

Multiply (1) by -2 to get -2x - 2y ≥ -60 Let this one be (3)

(Remember to reverse the inequality symbol when multiplying or dividing both sides of an inequality by a negative).

Now add (2) and (3) 2x - y ≥ -10

-2x - 2y ≥ -60

Now solve for y: -3y ≥ -70 and y ≤ 70/3 or 23 1/3; y ≥ 0 (Given)

Now solve for x by replacing y with 70/3 in (1)

x + 70/3 ≤ 30

Solve for x: x ≤ 90/3 - 70/3 or x ≤ 20/3 or 6 2/3; x ≥ 0 (Given)

Graph x≤20/3 and x≥0 and you get the horizontal line on the x-axis from 0 to 20/3.

Graph y≤70/3 and y≥0 and you get the vertical line on the y-axis from 0 to 70/3. The F.S. is the rectangular region formed by the corner points (0,0), (20/3, 0), (20/3, 70/3) and (0, 70/3).