Exercise 7.6.1 Classify the critical points of the following functions: (a) f(x, y ) = x2 +4y2 -2x + 8y-1 (c) f (x, y ) = xy (8) f(x,y) = xy(5x+ y-15) (i) f(x, y) = e-x/ 3+x-12Exercise 7.6.2 Find the ubsoiute maximum and minimum points of f : x2 + 331 3xy over the region bounded by y = x, y = O, and x = 2. Exercise 7.6.3 A six-sided rectangular box is to hold 1/2 cubic meter; what shape should the box be to minimize surface area? Exercise 7.6.4 A certain company produces and seiisat screen TVs. The total.r weekly revenue and cost in doiiars is given by R(x,y) = 0.2x2 0.25;;2 0.2xy + 225x+ 135y+ 1500, and C(x,y) = 125x + 45y + 5500 respectively, where x denotes the number of deluxe units and y the number of standard units produced and sold each week. Find the company 's maximum pmt per week, and the number of deluxe and standard units that must be produced and sold to achieve this prot.