A consumer consumes two (food) commodities, x and y. The consumer has utility function U(x,y) = 150-2(x-5)²- (y-5)² and faces the budget constraint p_xx + p_yy m.

a) Assuming m=15 and both prices are 1, find the optimal consumption plan (x*, y*).

b) Assuming m=10, y p =2 and 1 x p = , find the optimal consumption plan (x*, y*).