Question

maximize $ \sum_{i=0}^{n} x_{i} y_{i} $ Constraints $ \sum_{i=0}^{n} x_{i}=A $, where $ A $ is a constant $ \sum_{i=0}^{n} y_{i}=B $, where $ B $ is a constant \[ \begin{array}{l} 0 \leq x_{i} \leq A / 2 \\ 0 \leq y_{i} \leq B / 2 \end{array} \]

          maximize \( \sum_{i=0}^{n} x_{i} y_{i} \)
Constraints \( \sum_{i=0}^{n} x_{i}=A \), where \( A \) is a constant \( \sum_{i=0}^{n} y_{i}=B \), where \( B \) is a constant
\[
\begin{array}{l}
0 \leq x_{i} \leq A / 2 \\
0 \leq y_{i} \leq B / 2
\end{array}
\]

maximize ∑i=0^n xi yi
Constraints ∑i=0^n xi=A, where A is a constant ∑i=0^n yi=B, where B is a constant

0 ≤ xi≤ A / 2

0 ≤ yi≤ B / 2

Added by Atul L.

University Calculus: Early Transcendentals

Joel Hass, Christopher Heil, Przemyslaw… 4th Edition

Chapter 13

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Now, we know that the dot product of two vectors can be expressed in terms of their magnitudes and the angle between them: $$ \mathbf{x} \cdot \mathbf{y} = \|\mathbf{x}\| \|\mathbf{y}\| \cos \theta $$ Show more…

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