Answer Happy

6. For this problem, determine the function only. Do NOT solve the problem. This question is a test to see if you can determine the function. (I dislike giving a word problem that you have to solve, because if you can't set it up you can't solve it.) An entrepreneur is going to build heated storage rooms each shaped like a rectangular box. He wants each storage room to have a volume of 1000 cubic feet and be separated from each other in case of fire. Because warm air rises, the heat loss per unit of area through the ceiling is five times greater than the loss through the floor. The heat loss through the four walls is 3 times greater than the heat loss through the floor. Determine the function that you would use to find the room dimensions (for one of these storage rooms) that will minimize the heat loss. 7. Given that w = x?y z; x = s t2, y = 2s - t; and z = 3t. a) Construct a tree diagram illustrating the dependencies of the variables. Label edge of the diagram with the appropriate partial derivative. b) Using your diagram, write out the chain rule to determine the derivative of w with respect to s. aw c) Using the chain rule from part b, determine as' d) Write your answer to part c, in terms of sandt. aw e) Now, determine (in terms of s and t) by the same method. at