1. Erin's admission to a prestigious music school depends on the total score (Q) the admissions office decides to assign her. The school evaluates both her academic performance in high school and her skills as a musician. Hence, Q will be determined by the hours she spends on school work (S) and the hours she spends playing piano (P), her favorite instrument, every day. We can represent the total score using the following production function: Wi Q=S3P3. Answer the following: (a) To be admitted Erin needs a score of at least 3. Draw an isoquant curve for a total score of Q = 4 by placing school work, S, on the y-axis and piano practice, P, on the x-axis. To simplify, compute S for the points P =[1,4,16,64] and connect the dots. (b) In a day there are 24 hours and Erin knows that she needs to sleep at least 8 hours. Hence, assuming that she can allocate maximum 16 hours to work school and piano practice, write this constraint and provide a representation of this constraint on your graph. (c) Erin really wants to be admitted to her dream school, she prefers to focus time as long on piano practice as on school work (P=S), and she wants time to socialize outside of her duties. Is this possible? (Remember she has only 16 hours available; she needs to sleep too) (d) Find Erin's marginal productivity of school work, piano practice, and her MRTS of piano practice for school work (MP,/MPg)