Answer
There are 100 parents and 50 children.
Work Step by Step
Let the number of parents denoted by y and number of students reported by x. The equation from the first constraint is\[x+y\le 150\]. The equation from the second constraint is\[y-2x\le 0\]. Combine these two equations it could be seen that maximum number of parents is 100 and corresponding number of students is 50. Let the total amount of money which is the objective function be denoted by\[z\]. The equation for objective function is\[z=2y+x\].
The maximum or minimum of the objective function occur at the one or more of the corner points.
Solve the equation \[x+y=150\]and \[y-2x=0\];
So,
\[\begin{align}
& x+2x=150 \\
& 3x=150 \\
& x=50
\end{align}\]
Hence, \[y=100\]
In the same way, when student is 1, that is, \[y=1\] then,
\[\begin{align}
& x=150-1 \\
& =149
\end{align}\]
In the same way, when \[x=1\] then \[y=2\].
For the shaded region, put the point \[\left( 60,0 \right)\] in the inequalities \[x+y\le 150\] and\[y-2x\le 0\], then, \[60\le 150\]and \[-120\le 0\] which are true, so, the shade will be towards the point\[\left( 60,0 \right)\].
Evaluate the objective function at these corners provided below;
