need a solution in 15 minutes

Problem 1. Two consumers, Alice and Bob, have utility functions given by uA(x,y)=x1/2y1/4 and uB(x,y)=4x2+y2 respectively, where x and y are the number of apples and bananas respectively. Suppose that apples and bananas cost p1 and p2 dollars each respectively and that both consumers have M dollars to spend on apples and bananas. (a) On the same axes, sketch Alice's budget set and some contours uA(x,y)=c for positive values of c. By referring to your sketch explain why the method of Lagrange multipliers can be used to find the maximum value of uA(x,y) subject to her budget constraint. Hence use the method of Lagrange multipliers to find Alice's optimal bundle. (b) On the same axes, sketch Bob's budget set and some contours uB(x,y)=c For positive values of c. By referring to your sketch, find Bob's optimal bundle