Find carmen sandiegos utility by maximizing the choice of

Question

Carmen Sandiego receives utility from days spent traveling domestically (D) and days spent traveling internationally (F) as given by the utility function U(D;F) = D^1/2 F^1/2 . The price of a day of traveling domestically is Pd = $240 and in a foreign country Pf = $320. Carmen Sandiego's annual budget is $9600.

1. Find Carmen Sandiego's utility by maximizing the choice of domestic and foreign travel. Find her utility consuming that bundle. 
2. Suppose the price of domestic travel increases to PD = $300 per day. Find the new optimal bundle at this price as a function of her budget for traveling I: 
3. Find the income needed for Carmen Sandiego to reach the same utility as before the price change. 
4. Compute the quantities demanded with the new prices and the new income you found in part c) 
5. Compute the quantities demanded with the new prices and the original income. 
6. Decompose the changes in the quantity of D due to the income and substitution effects; illustrate with a graph. Give definitions of what the income and substitution effects mean.