Walter White is a notorious producer of methamphetamine. He is very precise and requires exactly 1 pound of Chemical X and 3 pounds of Chemical Y in each batch that he makes. Any ratio other than 1:3 yields an imperfect batch that Walter insists on throwing away. (a) (4) Write down a possible utility function for Walter as a function of q, and q, if his utility is equal to the number of batches that he makes - be careful with the coefficients here. (b) (3) Graphically illustrate a few of Walter White's indifference curves based on your utility func- tion in part (A). Which property of indifference curves do Walter's violate? (c) (4) If Walter has Y to spend on ingredients and prices are p, and py, what is Walter's demand for each product? (d) (4) Based on your answer to (C), how many batches can Walter produce if Y = $1,000, p = $40, and p = $20? (e) (3) At his optimal bundle that you calculated in part (D), what is Walter's MRS: how many pounds of Chemical Y would he be willing to sacrifice for one more pound of Chemical X?