The shaded region in the figure, which is unbounded, is the feasible region for x + y ≥ 6, 2x + y ≥ 8, x ≥ 0, y ≥ 0. What is the minimum value of Z = 4x + 3y? An unbounded shaded region in the first quadrant above the lines x + y = 6, 2x + y = 8, with corners (0, 8), (2, 4), (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 ≥ 6, 2x + y ≥ 8, x ≥…

Question 54

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The shaded region in the figure, which is unbounded, is the feasible region for $x + y \ge 6, 2x + y \ge 8, x \ge 0, y \ge 0$ . What is the minimum value of $Z = 4x + 3y$ ?

An unbounded shaded region in the first quadrant above the lines x + y = 6, 2x + y = 8, with corners (0, 8), (2, 4), (6, 0).

19

Correct answerYour answer

20

Correct answerYour answer

21

Correct answerYour answer

24

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Corners: $(0, 8)$ , $(2, 4)$ , $(6, 0)$ ; $Z$ there is $24$ , $20$ , $24$ .
The region is unbounded, so check that $4x + 3y < 20$ has no point in common with it: the line $4x + 3y = 20$ touches the region only at $(2, 4)$ .
So the minimum is $20$ .

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 ≥ 6, 2x + y ≥ 8, x ≥…

Question 54

Explanation