Answer
(a)
Provided that, a student earns when he spends x hours as tutor and y hours as teacher’s aide.
He gets \$10 per hour as tutor and $7 per hour as teacher’s aide.
So, the objective function that describes his total earning can be:
\[z=10x+7y\]
(b)
Provided constraints are:
Student cannot work more than 20 hours per week.
Tutor student must spent minimum of 3 hours per week.
Tutor student cannot spend more than 8 hours per week.
These three constraints can be described as system of inequalities as follows:
\[\left\{ \begin{align}
& x+y\le 20 \\
& \text{ }x\ge 3 \\
& \text{ }x\le 8 \\
\end{align} \right.\]
Work Step by Step
Since,
from part (d) the maximum value of objective function is 164 at \[\left( 8,12 \right)\].
So, refer part (d) to get the relevant values to fill in the blanks of the provided statement.
The student can earn the maximum amount by tutoring for 8 hours per week and working as a teacher’s aide for12 hours per week. The maximum amount that the student can earn each week is $164
