Given: The inequalities below
[tex]\begin{gathered} 2x+3y\leq18 \\ 5x+2y\leq23 \end{gathered}[/tex]
To Determine: The maximization of
[tex]\begin{gathered} P=5x+7y \\ x\ge0 \\ y\ge0 \end{gathered}[/tex]
Solution
The graph of the given inequalities is as shown below
The points the satisfing the maximization of all the equalities are
[tex]\begin{gathered} Point1:(0,0) \\ P=5x+7y=5(0)+7(0)=0+0=0 \\ Point2:(4.6,0) \\ P=5(4.6)+7(0)=23 \\ Point3:(0,6) \\ P=5(0)+7(6)=42 \\ Point4:(3,4) \\ P=5(3)+7(4)=15+28=43 \end{gathered}[/tex]
Hence, the maximum value of P is 43
