Solve clearly.

(7 points) Mary has the utility function: u(x, y) = xy + 1037. Mary's utility function represents strictly convex and strongly monotonic preferences for interior bundles. You do not need to check this. (a) (2 points) Find the utility maximizing bundle when the prices are px = 10, pi), = 10 and income M = 200. (b) (3 points) Presume that positive amounts of both good will be consumed (interior solutions). Find the utility maximizing bundles as functions of ALL relevant positive prices and income that are consistent with interior demands. (0) (2 points) Argue either: (i) that Mary's utility maximizing bundle will always be interior or (ii) that Mary's utility maximizing bundle will sometimes be non- interior. If you argue (ii), you must give all non-interior solutions and the prices and income levels that lead to them