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Maximise $Z=3 x+4 y$, subject to the constraints $x+y \leq 1$, $\mathrm{x} \geq 0, \mathrm{y} \geq 0$.
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Verified Answer
Maximise $Z=3 x+4 y$, subject to the constraints
$$
\mathrm{x}+\mathrm{y} \leq 1, \mathrm{x} \geq 0, \mathrm{y} \geq 0
$$
The co-ordinates of corner points $\mathrm{O}, \mathrm{A}$ and $\mathrm{B}$ are $(0,0)$, $(1,0)$ and $(0,1)$, respectively.
\begin{array}{|l|l|}
\hline Corner points & Value of \mathbf{Z} \\
\hline(0,0) & 0 \\
(1,0) & 3 \\
(0,1) & 4 \leftarrow Maximum \\
\hline
\end{array}
Hence, the maximum value of $Z$ is 4 at $(0,1)$
$$
\mathrm{x}+\mathrm{y} \leq 1, \mathrm{x} \geq 0, \mathrm{y} \geq 0
$$
The co-ordinates of corner points $\mathrm{O}, \mathrm{A}$ and $\mathrm{B}$ are $(0,0)$, $(1,0)$ and $(0,1)$, respectively.
\begin{array}{|l|l|}
\hline Corner points & Value of \mathbf{Z} \\
\hline(0,0) & 0 \\
(1,0) & 3 \\
(0,1) & 4 \leftarrow Maximum \\
\hline
\end{array}
Hence, the maximum value of $Z$ is 4 at $(0,1)$
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