Draw the feasible region for x + 2y ≤ 10, x + y ≤ 6, x ≤ 4, x ≥ 0, y ≥ 0, and find its corner points.

1. 1 · Write what is given and what is to be found. Given: three non-trivial constraints and x, y ≥ 0. To find: the feasible region and its corner points.
2. 2 · Draw the figure or sketch.
   • x + 2y = 10 through (10, 0) and (0, 5)
   • x + y = 6 through (6, 0) and (0, 6)
   • x = 4, a vertical line
   • O satisfies all three, so shade towards O; keep the first quadrant
3. 3 · Write the rule. Corner points are where two boundary lines meet; each must satisfy every constraint.
4. 4 · Find the corner points.
   • x = 4 and x + y = 6 give B(4, 2); check 4 + 4 = 8 ≤ 10
   • x + y = 6 and x + 2y = 10 give C(2, 4); check x = 2 ≤ 4
   • Also O(0, 0), A(4, 0) and D(0, 5); check D: 0 + 5 = 5 ≤ 6
5. 5 · Reject false corners. (4, 3), where x = 4 meets x + 2y = 10, breaks x + y ≤ 6, and (0, 6) breaks x + 2y ≤ 10. Neither is a corner.
6. 6 · Check and box the answer. Feasible region OABCD is bounded, with corners (0, 0), (4, 0), (4, 2), (2, 4), (0, 5).

Scoring tip: Label every line with its equation and every corner with its coordinates. Unlabelled graphs lose marks.