Answer:
The minimum value is [tex]18[/tex]
It occurs at [tex]P(6,0)[/tex]
Step-by-step explanation:
The given objective function is [tex]P(x,y)=3x+5y[/tex]
The vertices of the feasible region are [tex](0,7),(3,7),(6,3),(6,0)[/tex].
We plug in the vertices in to feasible region and evaluate to obtain,
[tex]P(0,7)=3(0)+5(7)[/tex]
[tex]P(0,7)=0+35[/tex]
[tex]P(0,7)=35[/tex]
[tex]P(3,7)=3(3)+5(7)[/tex]
[tex]P(3,7)=9+35[/tex]
[tex]P(3,7)=44[/tex]
[tex]P(6,3)=3(6)+5(3)[/tex]
[tex]P(6,3)=18+15[/tex]
[tex]P(6,3)=33[/tex]
[tex]P(6,0)=3(6)+5(0)[/tex]
[tex]P(6,0)=18+0[/tex]
[tex]P(6,0)=18[/tex]
