Linear Programming
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For the objective function \(P=3x+2y\) and the feasible region (shaded), determine the maximum value of \(P\)
\begin{align}
&\text{From the graph the points are}\\
&(0,0),(5,10) \text{ and } (10,0)\\
&\text{Objective function }\rightarrow P=3x+2y\\
&\text{At }(0,0) \quad P=0\\
&\text{At }(5, 10) \;\; P=35\\
&\text{At }(10,0) \;\; P=30\\
&\therefore \text{ Maximum of 35 occurs when } x=5 \text{ and } y=10.
\end{align}
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