Sarah receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D,F)=10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Sarah's annual travel budget is $4000.

6.1. Illustrate the indifference curve associated with a utility of 800 and the indifference curve associated with a utility of 1200. (Hint: To get the IC associated with utility of 800, set U(D,F)=800 and solve for D as a function of F, which will allow you to plot the indifference curve).

6.2. Graph Sarah's budget line on the same graph.

6.3. Can Sarah afford any of the bundles that give her a utility of 800? What about a utility of 1200?

6.4. Find Sarah's utility-maximizing choice of days spent traveling domestically and days spent in a foreign country. You are given that the marginal utility of domestic travel is MU_D=10F and marginal utility of foreign travel is MU_F=10D

Hint: You need to find the point where the slope of the budget constraint is equal to the slope of the indifference curve. Solve for D in terms of F; then plug it into the budget constraint to find B and F. This is equivalent to solving the following system of equations: