The extremium value of the function z = xy over the plane x + y = 1 is (upto two decimal places) _________.Correct answer is '0.25'. Can you explain this answer?

Question

Answer

The lagrangian function is given by

L = xy+ λ (x + y - 1)

Then L_x = y + λ = 0 i.e. λ = -y ........(i)

L_y = x + λ = 0 i.e. λ = -x ........(ii)

and x+ y - 1= 0 .......(iii)

From (i) and (ii), we have x = y

The from (iii), we have 2x - 1= 0 i.e. x=1/2

The critical point is x = y = 1/2, hence

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