(a) Use Lagrange multipliers to find the maximum value of
z = 4xy
subject to the constraint
x + 2y = 40
State the associated values of x, y and l.
(b) Repeat part (a) when the constraint is changed to
x + 2y = 41
(c) Verify that the value of the Lagrange multiplier in part (a) is approximately the same as the change in the optimal value of z when the right-hand side of the constraint is increased by 1 unit.