I need handwritten solution

Problem 4 A continuous function f : R2 -> R is defined by f(x, y) -81.2 + y. We wish to find the absolute extrema of f subject to the single constraint 4r' + 12 = 9. Remark: The constraint set is an ellipse, which is a closed and bounded subset of R2. (a) [5 points] Express this optimization problem as a Lagrange-multiplier problem. (b) [5 points] Show that either y = 0 or 1 = 1. Note: This does not necessarily mean that there are no values of A other than 1. (c) [5 points] Find all four solutions (x, y, A) of the Lagrange-multiplier problem. Hint: First consider the case y = 0. Then consider the case ) = 1. (d) [5 points] Find the absolute extrema of f subject to the constraint