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

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Answer 1 · 2018-03-12T09:25:43

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

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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)#