Toshi has entered a hotdog eating contest. Toshi estimates he can win the contest if he is able to consume eleven hotdogs within the time period allowed. Toshi actually likes hotdogs. His utility function is given by:
U(H) = 30H- .5H^2
Where H is the number of hotdogs consumed through a time interval equivalent to the contest period.
1. If Toshi wants to maximize his utility from the consumption of hotdogs, how many must he consume?
2. Use the lagrangean technique to decide Tosh's marginal utility of hotdogs when he consumes a total of eleven.