The shaded region in the figure is a feasible region. Which system of constraints gives it? A shaded region in the first quadrant with corners (0, 0), (3, 0), (3, 2), (0, 5), bounded by the lines x + y = 5 and x = 3 and the axes.

x + y ≤ 5, x ≤ 3, x ≥ 0, y ≥ 0

x + y ≥ 5, x ≤ 3, x ≥ 0, y ≥ 0

x + y ≤ 5, x ≥ 3, x ≥ 0, y ≥ 0

x + y ≤ 3, x ≤ 5, x ≥ 0, y ≥ 0

The shaded region in the figure is a feasible…

The shaded region in the figure is a feasible region.

MediumOriginal question

The shaded region in the figure is a feasible region. Which system of constraints gives it?

x + y \ge 5,\ x \le 3,\ x \ge 0,\ y \ge 0

Correct answerYour answer

x + y \le 5,\ x \ge 3,\ x \ge 0,\ y \ge 0

Correct answerYour answer

x + y \le 3,\ x \le 5,\ x \ge 0,\ y \ge 0

Correct answerYour answer

x + y \le 5,\ x \le 3,\ x \ge 0,\ y \ge 0

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The region contains the origin, so both boundary lines are ' $\le$ ' toward it.
Its corners $(0, 0)$ , $(3, 0)$ , $(3, 2)$ , $(0, 5)$ lie on $x + y = 5$ , $x = 3$ and the axes.

Worth noting

' $x + y \ge 5$ ' would put the region on the far side of the line, away from the origin.

Ten questions from Linear Programming, at your own pace.

Ten questions from Linear Programming, at your own pace.