Answer
100 parents and 50 students.
Work Step by Step
Step 1. Assume $x$ number of parents and $y$ number of students.
Step 2. Based on the given conditions, the total amount of money raised can be written as $z(x,y)=2x+ y$
Step 3. We can convert the constraints into inequalities as
$\begin{cases} x\geq0,y\geq0\\ x+y\leq150\\\frac{x}{2}\leq y \end{cases}$
Step 4. Graphing the above inequalities, we can find the vertices and the solution region as a triangular area in the first quadrant.
Step 5. With the objective equation and vertices, we have $z(0,0)=2(0)+(0)=0$, $z(100,50)=2(100)+(50)=250$, $z(0,150)=2(0)+(150)=150$,
Step 6. Based on the above results, we can find the maximum as $z(100,50)=250$ dollars with 100 parents and 50 students.
