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

Mar 12, 2018

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#### 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 $\left(4 , 1\right)$; f(x,y)=x-4y=4-4·1=0

For $\left(2 , 3\right)$; f(x,y)=x-4y=2-4·3=-10

For $\left(2 , - 1\right)$; f(x,y)=x-4y=2+4·1=6

So, the maximum value occurs in $\left(2 , - 1\right)$