For x + y ≥ 4, x ≥ 0, y ≥ 0, what is the maximum of Z = 3x + 2y?

Question 48

MediumOriginal question

For $x + y \ge 4$ , $x \ge 0$ , $y \ge 0$ , what is the maximum of $Z = 3x + 2y$ ?

12, at

(4, 0)

Correct answerYour answer8, at

(0, 4)

Correct answerYour answer0, at the originCorrect answerYour answerNo maximum existsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The region is everything on or above the line $x + y = 4$ in the first quadrant, which is unbounded.
Points like $(100, 0)$ are feasible and give $Z = 300$ ; $Z$ has no upper limit.

Worth noting

12 is the largest corner value, but on an unbounded region that settles nothing.

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