Assume that a consumer has the utility function U(x,y) = (3x+ 1)y, where x and y represent the quantities of two goods, X and Y.

Now assume that the consumer has S3 I to spend on goods X and Y, which have fixed prices of px=3 and py=4.

Calculate the consumption bundle (x,y) that solves the first-order condition for the consumer's problem.

Calculate the two consumption bundles (x,y) that are on the boundary of the consumer's optimization problem.

For the three possible solutions that you found in parts (f) and (g), calculate the utility that the consumer would receive from each bundle.

What should she do to maximize her utility? Justify your answer carefully.