Please show math:

B. Suppose your tastes for "square feet of housing" (x,) and "other goods" (x2) can be represented by the utility function u(x1,X2) = X1X2. a. Calculate your optimal housing consumption as a function of the price of housing (p,) and your exogenous income / (assuming of course that p2 is by definition equal to 1). b. Using your answer, verify that you will purchase a 2,000-square-foot house when your income is $400,000 and the price per square foot is $100. C. Now suppose the price of housing falls to $50 per square foot and you choose to sell your 2,000-square-foot house. How big a house would you now buy? d. Calculate your utility (as measured by your utility function) at your initial 2,000-square-foot house and your new utility after you bought your new house. Did the price decline make you better off? e. How would your answers to B(c) and B(d) change if, instead of falling, the price of housing had increased to $200 per square foot