Suppose you have utility function U (x, y) = ( x-1)(y-5). The price of good x is $2 and the price of good y is $2. You have $4 dollars to spend. You wish to find your optimal consumption bundle. (in other words you wish to solve the following maximization problem)

max U (x, y) = (x-1)(y -5) x,y

s.t. 2x + 2y = 4

What is the tangency condition?

What is the optimal bundle (x* y*)? (hint: consider the possibility of a corner solution)

PLEASE SHOW ALL WORK