An online dating service is trying to determine how to allocate funds for advertising. The manager decides to advertise on the radio and through internet ads. Previous experience with such advertising leads the dating service to expect for. n) = 0.8r2n responses when r ads are run on the radio and n intemet ads are run. Check: 10,30):2400 Each ad on the radio costs $152, and each internet ad costs $76 and the dating service has budgeted $7752 for advertising, so the advertising constraint is gifr, n) = 152M76n=7752 dollars. (a) Choose the system of equations that could be used to nd the optimal number of responses subject to the advertising constraint. 1.6m = ll 1.6m + 152.1 = O 1.6m = a 1.6m = 15211 O 0.512 = .l O 0.13:2 + 75.1 = o O 0-8:"2 = 0 0.572 = 75). 152i' + 76a = 7752 152- + 76m = 7752 152' + 75" = 7752 152r + 76:1 = 7752 'I 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=34, 11:34, 1:12.168, and {=31443.2 . (b) Use the close-point method to classify the optimal point. (Do NOT round.) r n (Tan) Close point 1 33 |:| \\:| Optimal point 34 34 31443.2 Close point 2 |:| 33 \\:| The optimal polnt is a . (c) Suppose the manager budgeted an addltional $70 for advertising. Use the solution that was previously given to estimate the resulting change in the optimal value. \\:I additional responses (Round to the nearest whole number.)