Erica has written a best-seller. Revenues (net of production costs) are equal to 300*(T^{1/3})*(A^{1/3})

where T is the number of publicity trips Erica takes and A is the number of ads for the book that appear.

Erica has to pay for all of her own publicity trips, which cost $100 each. Her publisher pays for the advertising, which costs $100 per ad. Revenues from the book are split equally between Erica and her publisher.

(i) What are the number of publicity trips that Erica would make in a Nash equilibrium in which Erica chose the number of trips and the publisher chose the amount of advertising?

(ii) What would be the number of trips that Erica should make if trips and advertising are determined jointly in order to maximize total profits net of trip and ad costs?