Question

Find the maximum and minimum values of f(x,y) = 8x+y for the polygonal convex set having vertices at (0, 0), (4, 0), (3, 5), (0, 5).

Answer 1

F(x,y)=8x+y

This means, f is a function where we plug in pairs of numbers.
then, f calculates the first number times 8, to which it then adds the second number we plugged.

let's calculate f for the vertices:

f(0,0)=8*0+0=0+0=0

f(4, 0)=8*4+0=32+0=32

f(3, 5)=8*3+5=24+5=29

f(0, 5)=8*0+5=0+5=5

the maximum value of f is 32
the minimum value of f is 0