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# a7 - University of Toronto at Scarborough Department of...

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University of Toronto at Scarborough Department of Computer & Mathematical Sciences MATA33 Assignment 7 Winter 2008 Quiz 7 is based on this assignment and the relevant text readings and lecture notes. Quiz 7 will be written in the 8th tutorial, which takes place during the week of March 10 - 14. Study: Sections 17.3 and 17.4 for this assignment (reviewing sections 17.1 and 17.2 would be useful too). Read ahead in Sections 17.5 and 17.6. Problems: 1. Section 17.3, Pages 759 - 761 # 1, 2, 4 - 10, 14, 18 - 20. 2. Section 17.4, Page 763 # 1, 2, 5, 6, 10, 11, 13, 14, 16, 19. 3. Find the equation of the horizontal plane that is tangent to the graph of the function z = G ( x, y ) = x 2 - 4 xy - 2 y 2 + 12 x - 12 y - 1 . (Hint: review the general form of a plane in 3-dimensional space as stated at the bottom of page 748). 4. Let P ( x, y ) = xy ax + by where P represents profit; x, y > 0 represent sales of products X and Y (respectively); and a, b > 0 are constants. Show that the sum of the marginal profits when x = y is equal to 1 a + b 5. Throughout this problem use the function in #24 on page 796 (a) Do problem # 24 on page 796 (b) Verify the concept of marginal as outlined at the top of page 756. That is, verify that
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