Given,
The function is,
P = 3x + 5y
The constraint are,
[tex]\begin{gathered} x\ge0 \\ y\ge0 \\ x+y\leq5 \\ 3x+6y\leq21 \end{gathered}[/tex]
The graph of the inequalities is,
The maximum value is,
At (0, 3.5)
[tex]P=3x+5y=3\times0+5\times3.5=17.5[/tex]
At (3, 2)
[tex]P=3x+5y=3\times3+5\times2=19[/tex]
At (5, 0)
[tex]P=3x+5y=3\times5+5\times0=15[/tex]
Hence,the maximum value is 19.
