The shaded region in the figure, which is unbounded, is the feasible region for x + 2y ≥ 6, 3x + y ≥ 8, x ≥ 0, y ≥ 0. What is the minimum value of Z = 3x + 2y? An unbounded shaded region in the first quadrant above the lines x + 2y = 6, 3x + y = 8, with corners (0, 8), (2, 2), (6, 0).

The shaded region in the figure, which is…

The shaded region in the figure, which is unbounded, is the feasible region for x + 2y ≥ 6, 3x + y ≥ 8, x ≥…

Question 55

HardOriginal question

The shaded region in the figure, which is unbounded, is the feasible region for $x + 2y \ge 6, 3x + y \ge 8, x \ge 0, y \ge 0$ . What is the minimum value of $Z = 3x + 2y$ ?

An unbounded shaded region in the first quadrant above the lines x + 2y = 6, 3x + y = 8, with corners (0, 8), (2, 2), (6, 0).

9

Correct answerYour answer

10

Correct answerYour answer

16

Correct answerYour answer

18

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Corners: $(0, 8)$ , $(2, 2)$ , $(6, 0)$ ; $Z$ there is $16$ , $10$ , $18$ .
The region is unbounded, so check that $3x + 2y < 10$ has no point in common with it: the line $3x + 2y = 10$ touches the region only at $(2, 2)$ .
So the minimum is $10$ .

Worth noting

On an unbounded region the largest corner value is not a maximum: $Z$ can grow without limit.

Concept: Checking a minimum with the half-plane test
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsUnbounded and infeasible problems

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Ten questions from Linear Programming, at your own pace.

Practise this chapter →

Ten questions from Linear Programming, at your own pace.

The shaded region in the figure, which is unbounded, is the feasible region for x + 2y ≥ 6, 3x + y ≥ 8, x ≥…

Question 55

Explanation