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【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/2Consider the objective functionf(x,y)=xyLet the constraint function be g(x,y)=y−e4xExplanation:ExplanationApply Lagrange Multiplier as follows:  Δf(x,y)=λΔg(x,y)So, find the gradients both sides and equate as,<y,x>=λ<−4e4x,1>Equate both sides to obtain, y=−λ4e4x,x=λSubstitute lamda=x in equationy= ... See the full answer