Find Olivia's optimal consumption bundle (x* ,y* ) associated with the following utility functions. Her income is I, and the prices of good x and y are respectively p and 1. Moreover, the goods must be nonnegative.

a. Her utility function is u(x,y) =xy/(x+y) subject to px + y I, x 0, y 0. Make sure you are clear about how to apply the Lagrangian method.

b. Her utility function is u(x, y) =x + xy, subject to px + y I, x 0, y 0. Hint: there are corner solutions to this problem.