University of Toronto at ScarboroughDepartment of Computer & Mathematical SciencesMATA33Assignment 7Winter 2008Quiz 7 is based on this assignment and the relevant text readings and lecture notes.Quiz 7 willbe 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 usefultoo). 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 functionz=G(x, y) =x2-4xy-2y2+ 12x-12y-1 . (Hint: review the general form of a plane in3-dimensional space as stated at the bottom of page 748).4. LetP(x, y) =xyax+bywherePrepresents profit;x, y >0 represent sales of productsXandY(respectively); anda, b >0 are constants. Show that the sum of the marginal profits whenx=yis equal to1a+b5. 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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