Question

If `x>=2, y-x>=-3, and x+y<=5`, what is the maximum value of `f(x,y)=x-4y`?

Answer 1

See details below

Explanation:

First, we have to draw the interception of three given conditions. We have something like this:

Where the intercpetions points are `(4,1);(2,3) and (2,-1)`

By a famous theorem, we know that maximum values of a linear funtion lies in intersection points of restriction area. Thus we proof with this values

For `(4,1)`; `f(x,y)=x-4y=4-4·1=0`

For `(2,3)`; `f(x,y)=x-4y=2-4·3=-10`

For `(2,-1)`; `f(x,y)=x-4y=2+4·1=6`

So, the maximum value occurs in `(2,-1)`