On your next vacation, you will divide lodging between large resorts and small inns. Let x represent the number of nights spent in large resorts. Let y represent the number of nights spent in small inns.

a. Write a system of inequalities that models the following conditions: You want to stay at least 5 nights. At least one night should be spent at a large resort. Large resorts average $200 per night and small inns average $100 per night. Your budget permits no more than $700 for lodging.

b. Graph the solution set of the system of inequalities in part (a).

c. Based on your graph in part (b), what is the greatest number of nights you could spend at a large resort and still stay within your budget?