Check each constraint equation one at a time to reveal its solution. When all four constraints have been graphed, use the green "polygon" tool to highlight the vertices of a polygon whose graph is the feasible region for all possible combinations of cats and dogs Carlos and Clarita can board and still meet the four constraints.
The profit equation, p=8c+20d, represents the amount of money Carlos and Clarita can make each day for boarding different combinations of cats and dogs. Select a desirable profit and enter it for p. Can Carlos and Clarita earn that amount each day? How does your representation help you answer that question? Change the value of p until you are convinced you have found the number of cats and dogs that will allow Carlos and Clarita to earn the most each day. (Note: This is really a revenue equation, rather than a profit equation, since Carlos and Clarita also have to consider their costs each day.)