The equation is given to be:
[tex]P=3x+y[/tex]
The inequalities used as a constraint for the equation are given to be:
[tex]\begin{gathered} x\ge0 \\ x\le4 \\ y\ge-1 \\ y\le5 \end{gathered}[/tex]
To optimize the equation, we will plot the inequalities using a graphing tool. The graph is shown below:
The white region of the graph represents the solution space.
The vertices of the graph will be used to optimize the equation. These are:
[tex](x,y)=(0,5),(4,5),(0,-1),(4,-1)[/tex]
At (4, 5):
[tex]P=3(4)+5=12+5=17[/tex]
At (0, 5):
[tex]P=3(0)+5=5[/tex]
At (0, -1):
[tex]P=-1[/tex]
At (4, -1):
[tex]P=11[/tex]
Therefore, the maximum value of P is 17.
The SECOND
