A consumer has the utility function U(x,y) = (y+10)x + 4y, where x>=0 and y>=0 represent her consumption of goods X and Y.(a) Calculate the marginal utility of good X and the marginal utility of good Y.
(b) Assume that the consumer has I=$100 to spend on goods X and Y. The price of goodX is Px=$7 per unit, and the price of good Y is Py=$4 per unit. Calculate the consumer's highest possible utility and the consumption bundle (x,y) that achieves that utility. You should show your reasoning and justify your answer carefully.