6) Prepare a graph of the constraints and objective function and solve the following litioar prograthming problem: (20 points). Maximize: f=2x1x2 Subject to constraint 1:x1+x22 constraint 2:x1+x25 constraint 3:x1x21 constraint 4:x1+x24 constraint 5:x10 constraint 6:x20 Hints: Draw the line of each constraint on the graph below (two constraints are already drawn) After drawing all the lines shade the optimal region. Try f=0,f=2 and f=4. Which one is the optimum, and what are the values of x1 and x ? 2) A spherical balloon is being inflated at a constant rate of 240cm3s1. (20 points) (a) At what rate is the radius increasing when the radius is 8cm ? (b) At what rate is the radius increasing after 5 seconds