The shaded region in the figure, which is unbounded, is the feasible region for x + y ≥ 4, x + 3y ≥ 6, x ≥ 0, y ≥ 0. What is the minimum value of Z = 2x + 3y? An unbounded shaded region in the first quadrant above the lines x + y = 4, x + 3y = 6, with corners (0, 4), (3, 1), (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 + y ≥ 4, x + 3y ≥ 6, x ≥…

Question 47

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The shaded region in the figure, which is unbounded, is the feasible region for $x + y \ge 4, x + 3y \ge 6, x \ge 0, y \ge 0$ . What is the minimum value of $Z = 2x + 3y$ ?

An unbounded shaded region in the first quadrant above the lines x + y = 4, x + 3y = 6, with corners (0, 4), (3, 1), (6, 0).

9

Correct answerYour answer

10

Correct answerYour answer

11

Correct answerYour answer

12

Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

Corners: $(0, 4)$ , $(3, 1)$ , $(6, 0)$ ; $Z$ there is $12$ , $9$ , $12$ .
The region is unbounded, so check that $2x + 3y < 9$ has no point in common with it: the line $2x + 3y = 9$ touches the region only at $(3, 1)$ .
So the minimum is $9$ .

Worth noting

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

Concept: Minimum over an unbounded region
Typical timeTypical: 90 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 + y ≥ 4, x + 3y ≥ 6, x ≥…

Question 47

Explanation