IMPORTANT: If youre going to write please make sure your writing is neat and easy to read. Please write in print (not cursive).Please give a detailed explanation for your answers. Thank you

IMPORTANT: I already figured out the answers for parts a-d. I will put my answers beneath the qauestions in case you need them. PLEASE DO NOT ANSWER PARTS A-C. I ONLY NEED HELP WITH PARTS D-F. Please give a through, easy to understand, step by step explanation for those parts. Thank you!

a. How will Bilbo choose to allocate his labor?

ANSWER: (9/2)ln(L_berries)+8ln(L_stones)

b. What will the optimal levels of berries and stones be?

ANSWER: B*=6; S*=64

c. What will Bilbos utility be?

ANSWER: 9ln(6)+8ln(64)=49.4

THIS POINT FORWARD IS WHERE I ACTUALLY NEED HELP. PLEASE ONLY HELP ME FROM D-F. Thank you!

(2) On Bilbo's quest, the rest of the group decided that he was holding them back, so one morning, they left him stranded in the Mirkwood Forest. Bilbo is able to work 100 hours a week. He can split this time between gathering magical stones and gathering berries. His production functions are: Berries = Laborberries Stones = L Stones And his utility function is: U = 9 In(B) + 8 In(S) d. Suppose a group of elves encounters Bilbo in the woods. Since elves are magical, the magical stones have little value to them: they will trade with Bilbo at a price ratio of Pb/Ps = 16/7. If Bilbo continues his production from part a, what will he choose to consume now that he can trade? What will be his level of utility? (Hint: Think about which parts of Bilbo's utility- maximizing Langrangian function will change in the face of new prices.) e. Now, Bilbo realizes that, if he changes his production, he can increase his utility further. How does Bilbo choose to change his production to maximize his utility? What is his consumption? What is his utility? (Hint: You will first need to maximize Bilbos income before maximizing his utility.) f. Draw a graph illustrating your answers. This graph should feature the consumption of Bilbo at points A, D, and E. It should also include the PPF for Bilbo as well as two lines indicating the potentialities of trade between Bilbo and the elves in parts D and E