Chapter 8.6, Problem 16E

a. A student earns $15 per hour for tutoring and $10 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 $_________.