5. When Katerina goes running, she can either take water (W) or coconut water (C) with her to drink. She believes coconut water is three time more hydrating than plain water. Katerina just cares about the hydrating power of the drink.

(i) Can Katerina's utility function be represented by U(W,C) =3C + W? (10 marks)

(ii) Given U(W,C) =3C + W, Katerina has 28 pounds to spend on these two drinks. If a bottle of water costs 1 and a bottle of coconut water costs 2, what is Katerina's optimal choice? Note that MU_w = 1 and MU_c=3. (10 marks)

(iii) Explain under which conditions the tangency condition does not work. Given that the tangency condition does not work, discuss how we can find out the optimal consumption bundle for a consumer. (20 marks)