Sarah has a monthly income of 500 dollars that she spends buying food that costs 5 dollars, clothes that cost 20 dollars, and books that cost 50 dollars.
Sarah's utility function is given by: U(F, C, B) = 6ln(F) + 2ln(C) + ln(B)
a. Write down Sarah's budget constraint.
b. Compute the marginal rate of substitution of books for clothing ( UB/UC ) and books for food ( UB/UF ).
c. Find her optimal allocation.