Font 3. (5 points total). Use a Lagrange multiplier to optimize the following function subject to the given constraint and estimate the effect on the value of the value of the objective function from a 1-unit change in the constant of the constraint (i.e. obtain solution, substitute, and evaluate the function, take note of Lagrange multiplier value). Z = 4x2 - 2xy + 6y2 s. t. xty = 72 Then, solve the same problem with the constraint modified to be: xty= 73 Explain what you find. What is the meaning of the Lagrange multiplier? 4. (5 points total). Suppose we have the following risk-neutral probability and up and down movements for a binomial lattice:: erat d q = u- d u = evAt d = e-ovAt Show that the discounted asset value is a martingale. Hint, you can substitute and use basic algebra to show that under the risk-neutral measure the expectation F = So = erAt S, (i.e. that is, under the risk-neutral measure Q, the value one-period prior is equal to the discounted value one-period hence). 1232 WORDS WU QUAL 5. (5 points total). With a binomial lattice where we wish to model asset prices such that, X