We have a feasibility region and we have to find at which point of the region the function P can be maximized:
[tex]P=3x+2y[/tex]
As this is a linear function, the maximum value will be in one of the vertices of the region. We can identify the vertices as:
We can calculate the value of P for each of the vertices and see which one has a maximum value. We can already guess that P(8,0) will be greater than P(0,8) as the coefficient for x is greater than the coefficient for y.
We can calculate the three values as:
[tex]\begin{gathered} P(0,8)=3\cdot0+2\cdot8=0+16=16 \\ P(6,5)=3\cdot6+2\cdot5=18+10=28\longrightarrow\text{Maximum} \\ P(8,0)=3\cdot8+2\cdot0=24+0=24 \end{gathered}[/tex]
Answer: the maximum value of P is 28.
