(a) Draw the region R consisting of points (x, y) = R² satisfying x ≥ 1, y ≥ 1, x + y ≥ 3. Find the point in R minimizing 4x + 3y. Is there a point where it is maximized?

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Exercise 12.9.
(a) Draw the region R consisting of points (x, y) = R² satisfying x ≥ 1, y ≥ 1, x + y ≥ 3. Find the
point in R minimizing 4x + 3y. Is there a point where it is maximized?
(b) Draw the parallelogram formed with vertices 0, v = [2].
-3].
4x + 3y is maximized on this parallelogram, and compute its maximal value.
(c) Minimize -x + 2y on the parallelogram in (b), and compute its minimal value.
W=
and v + w.
Identify where
Transcribed Image Text:Exercise 12.9. (a) Draw the region R consisting of points (x, y) = R² satisfying x ≥ 1, y ≥ 1, x + y ≥ 3. Find the point in R minimizing 4x + 3y. Is there a point where it is maximized? (b) Draw the parallelogram formed with vertices 0, v = [2]. -3]. 4x + 3y is maximized on this parallelogram, and compute its maximal value. (c) Minimize -x + 2y on the parallelogram in (b), and compute its minimal value. W= and v + w. Identify where
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