1. (25 points + 2 bonus) If an artist reads x volumes of literature and watches y lms, then they will be inspired to make 1 g+4lnx+4lny pieces of art. The q 2 0 is the quality of literature (observe the higher the q, the more inspired the artist from reading a fixed amount of literature). The artist knows the value of q but cannot change it. Each volume of literature costs 6 and movie 2. The artist how many volumes of literature to buy and read as well as how many movies to buy and watch. Their goal is to minimise costs while ma king 5 art pieces. a) (4 points) Formally write the constrained optimisation problem. b) (5 points) Using the Lagrangian method, nd an equation linking optimal volumes of literature read x*to literature quality q (your expression should only have these two variables). c) (2 points) In words, what does x'o[q) represent? d) (5 points) Do optimal volumes of literature increase or decrease in q? Justify your answer with math. e) (2 points) Bonus: Using economic intuition, interpret your previous answerwhy does x* increase or decrease in q? For the rest of the problem, suppose that q = 0. f) (5 points) What is the optimal number of volumes read? The optimal number of lms watched? Justify your answer. g) (3 points) The artist now aims to make 4 pieces of art. Without resolving the optimisation problem, do minimised costs increase or decrease? By approximately how much