$f(r,n)=0\mathrm{.}3r^{2}n$ responses

when $r$ ads are run on the radio and $n$ internet ads are run. Check: $f(10,30)=900$

Each ad on the radio costs $$124,$ and each internet ad costs $$62$ and the dating service has budgeted $$6138$ for advertising, so the advertising constraint is

$g(r,n)=124r+62n=6138$ dollars.

$($a$)$ Choose the system of equations that could be used to find the optimal number of responses subject to the advertising constraint.

$0\mathrm{.}6rn=$

$0\mathrm{.}6rn+124=0$

$0\mathrm{.}6rn=124$

$0\mathrm{.}6rn=0$

$0\mathrm{.}3r^2=$

$0\mathrm{.}3r^2+62=0$

$0\mathrm{.}3r^2=62$

$0\mathrm{.}3r^2=0$

$124r+62n=6138$

$124r+62n=6138$

$124r+62n=6138$

$124r+62n=6138$

You do NOT need to solve the system. The solution is provided.

The optimal point subject to the constraint was found to occur where:

$r=33,n=33,=5\mathrm{.}269,$ and $f=10781\mathrm{.}1.$

$($b$)$ Use the close$-$point method to classify the optimal point.

$($Do NOT round.$)$

The optimal point is a $---$ Select$---$ because the value of $f$ at this point is $---$ Select$---$ the value of $f$ at each of the nearby points on the constraint.

$($c$)$ Suppose the manager budgeted an additional $$100$ for advertising. Use the solution that was previously given to estimate the resulting change in the optimal value

additional responses $($Round to the nearest whole number.$)$