6. In Cowie's (19??) article, the optimal time in patch must satisfy the optimality condition dftTD 2 fat) 031\" T; +1"; ' p (a) Show how this optimality condition is derived. (b) Interpret this optimality condition diamgatically and intuitively. (c) What will happen to the optimal time in patch T; if the size of the room in Cowie's experiment is enlarged so that the interpatch travel time I} is quadrupled? Will the time in patch he quadrupled, unchanged, or quartered? Prove your answer mathematically and interpret it diagrammatically and intuitively. (d) What will happen to the optimal time in patch T; if the size of the patch in Cowie's experiment is enlarged and more mealwonns are put in each patch so that the net energy gain function becomes f{Tp) = 4Q(le'm1l)? Will the time in patch he quadrupled, unchanged, or quartered? Prove your answer mathematically and interpret it diagrammatically and intuitively