Find the corner points of the feasible region for x + y ≤ 7, x ≤ 5, y ≤ 4, x ≥ 0, y ≥ 0. Say whether (3, 3) and (5, 3) are feasible solutions.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write what is given and what is to be found. Given: x + y ≤ 7, x ≤ 5, y ≤ 4, x ≥ 0, y ≥ 0. To find: the corners, and whether (3, 3) and (5, 3) are feasible.
2 · Draw the figure or sketch. Draw x + y = 7 through (7, 0) and (0, 7), the vertical line x = 5 and the horizontal line y = 4. Shade towards O for all three.
3 · Write the rule. A corner is where two boundary lines meet and all the constraints still hold.
4 · Find the corner points.
x = 5 and x + y = 7 give (5, 2)
y = 4 and x + y = 7 give (3, 4)
Also (0, 0), (5, 0) and (0, 4)
(5, 4) breaks x + y ≤ 7, so it is not a corner
5 · Test the two points.
(3, 3): 6 ≤ 7, 3 ≤ 5, 3 ≤ 4, so it is feasible
(5, 3): 8 > 7, so it is infeasible
6 · Check and box the answer. Corners: (0, 0), (5, 0), (5, 2), (3, 4), (0, 4). (3, 3) is feasible; (5, 3) is not.
Scoring tip: Check each corner in every constraint. A crossing of two lines outside the region is not a corner.
