Name: Section: MATH 25 Unit 4 Problem Set Directions: Answer the following COMPLETELY, NEATLY, and ORDERLY. Submit your answers (in pdf format) through our google classroom. 1. The volume V of a right circular cone of radius r and height h is given by V = 31 πr2 h. (2 points each) (a) Find a formula for the instantaneous rate of change of V with respect to r if r changes and h remains constant. (b) Find a formula for the instantaneous rate of change of V with respect to h if h changes and r remains constant. 2. Given f (x, y, z) = xexy + sin(xyz), find fyzz . (7 points) 3. A manufacturer supplies refrigerators to two stores, A and B. The manager estimates that if x refrigerators are delivered to store A and y units to store B each month, the monthly profit will be P (x, y) pesos, where P (x, y) = −2x2 − 3xy − 2y 2 + 20x + 40y − 300. Each month, the company can produce exactly 700 refrigerators. How many refrigerators should be supplied to store A and how many to store B in order to maximize monthly profit? (7 points) 4. LetR be the region shown in the accompanying figure. Fill in the missing limits of integration. (8 points) ZZ Z 4Z Z 5Z (a) f (x, y) dA = f (x, y) dydx + f (x, y) dydx R 2 ZZ Z 4 Z f (x, y) dA = (b) R f (x, y) dxdy 5. SET-UP the double integral that solves for the volume of the solid z = 9 − x2 − y 2 on the first octant using dydx. (4 points) Total: 30 pts 2