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The purpose of this exercise is to provide practice using Excel Solver or LINGO. Find the values of X and Y that minimize the

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\small \\$Given that\\$ X^2-8X+Y^2+2Y+10\\ $We need minimize the given function\\$ X^2-8X+Y^2+2Y+10\\ =X^2-2\times X\times4+Y^2+2\times Y\times1+16+1-7\\ =X^2-2\times X\times4+16+Y^2+2\times Y\times1+1-7\\ =X^2-2\times X\times4+4^2+Y^2+2\times Y\times1+1^2-7\\ =(X-4)^2+(Y+1)^2-7\\ $Minimum possible value for $(X-4)^2,(Y+1)^2 $ are 0,0 respectively$\\ Min(X^2-8X+Y^2+2Y+10)=0+0-7=-7\\ X-4=0,Y+1=0\Rightarrow X=4,Y=-1\Rightarrow (X,Y)=(4,-1)

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