Mary obtains utility from days spent traveling on holiday domestically (D) and days spent traveling in a foreign country (F) as denoted by the utility U(D, F) = DF. The price of a day spent traveling domestically is 250 and in a foreign country 200. Marys annual budget for traveling is 10,000. [44 marks]

(1) Find Marys utility maximizing choice of days traveling domestically and in a foreign country. Find also her utility level from consuming that bundle. [12 marks]

(2) Suppose that the price of domestic traveling decreases to 160 per day. Assuming her budget for traveling x (unknown) find the demand for D and F under the new prices as a function of x. [12marks]

(3) Find x for Mary to reach the same utility level as before the price change. [8 marks]

(4) Compute the quantities demanded with the new prices and the income from Question (3).