- You must work for at least 80 hours in this course to complete the requirements. Some of that will be testing time, and some will be for assignments. You have 18 tests that take from 1/2 hour to 2 hours each to complete. You have 110 assignments that take between 1/2 hr and 1 hour to complete.

- Write the five inequalities involved.
- Graph the system of inequalities.
- Choose a point that satisfies the constraints, and write a short paragraph about why you will devote these times to testing and assignments.
Help:

- One of the constraints is testing. Use x for the testing variable and y for the assignment variable. There are a total of 5 inequalities to write. 18 tests for 1/2 hour is 9 hours minimum. 18 tests for 2 hours each is 36 hours maximum. This gives you x
>9 and x<36. Now write the inequalities that describe the time spent on assignments. The last inequality is the one for the

total number of hours spent in the course (x + y).- Once you have the inequalities, you will need to graph them on the same coordinate plane in order to find the area of intersection. If you are going to attempt to graph this system by hand, be sure to use appropriate tick marks on your coordinate plane. You may want to count by 5's so your graph will not be too big.
- The solutions to the system of inequalities are all the points in the overlapping shading areas. For example, you may work 20 hours on tests and quizzes and 100 hours on assignments. It is possible that due to your work on the assignments, you do not have to spend as much time on your quizzes and tests. Since 100 plus 20 is greater than 80 hours, you are meeting the total hour constraint as well.

- The school system is trying to help their students be more successful. They are going to hire tutors to help. They must have 20 teachers to have the correct student/teacher ratio. There must be no more tutors than teachers. The maximum number of people to be hired is 50. How many tutors and how many teachers should they hire?

- Write the inequalities for the above constraints.
- Graph the system of inequalities.
- Choose a point that satisfies the constraints, and write a short paragraph about why you chose that number of tutors and teachers.
Help:Use x for teachers and y for tutors. There will be a total of three inequalities in this system.