Chapter 8.6, Problem 16E

a. A student earns $10 per hour for tutoring and $7 per hour as a teacher’s aide. Let x = the number of hours each week spent tutoring and let y = the number of hours each week spent as a teacher’s aide. Write the objective function that models total weekly earnings.

b. The student is bound by the following constraints:

• To have enough time for studies, the student can work no more than 20 hours per week.

• The tutoring center requires that each tutor spend at least three hours per week tutoring.

• The tutoring center requires that each tutor spend no more than eight hours per week tutoring.

Write a system of three inequalities that models these constraints.

c. Graph the system of inequalities in part (b). Use only the first quadrant and its boundary, because x and y are nonnegative.

d. Evaluate the objective function for total weekly earnings at each of the four vertices of the graphed region. [The vertices should occur at (3,0), (8,0), (3,17), and (8,12).]

e. Complete the missing portions of this statement: The student can earn the maximum amount per week by tutoring for ____ hours per week and working as a teacher’s aide for____ hours per week. The maximum amount that the student can earn each week is $___.