Textbook Problem

Advertising A private golf club is determining how to spend its $8100 advertising budget. The club knows from prior experience that the number of responses A is given by

$A=0.0001t^{2}p{r}^{1.5}$ where t is the number of cable television ads, p is the number of newspaper ads. and r is the number of radio ads. A cable television ad costs $90, a newspaper ad costs $36, and a radio ad costs $45.

(a) How much should be spent on each type of advertising to obtain the maximum number of responses? (Assume the golf club uses each type of advertising.)

(b) What is the maximum number of responses expected?