Chapter 5.6, Problem 16PE

(a)

To determine

The objective function that models the total weekly earnings of a student who earns $10 per hour for tutoring and $7 per hour as a teacher’s aide.

(b)

To determine

The system of inequalities that models the following constraints: Student cannot work for more than 20 hours a week, he has to spend at least 3 hours a week as tutor, he cannot spend more than 8 hours tutoring per week.

(c)

To determine

To graph: The system of inequalities obtain in the part (b), that is $x+y\le 20,x\ge 3$ and $x\le 8$.

(d)

To determine

To calculate: The value of the objective function $E=10x+7y$ at the vertices $\left(3,0\right),\left(8,0\right),\left(3,17\right)$ and $\left(8,12\right)$ of the common shaded region obtained in the part (c).

(e)

To determine

To fill: The blank spaces in the statement, “The student can earn maximum amount per week by tutoring for _______ hours per week and working as teacher’s aide for ______ hours per week. The maximum amount student can earn each week is _____.”.