6. Maximize Q = xy, where x and y are positive numbers such that x + 3y* = 16. Write the objective function in terms of y- Q = "Type an expression using y as the variable.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) The maximum value of Q is (Simplify your answer.) 7. A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 700 yd of rope and floats. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the shoreline is one side of the rectangle.) Let x be the length of a side of the rectangle perpendicular to the shoreline. Write the objective function for the area in terms of x. A(x) = (Type an expression using x as the variable.) The length of the shorter side of the rectangular region is (1) The length of the longer side of the rectangular region is (2) The maximum area of the rectangular region is (3) (1) O yd. (2) O yd. (3) O yd. O yd'. O yds. O yds. O yaz. O yd. 8. Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 43 in. by 23 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume. The dimensions of box of maximum volume are (1). Round to the nearest hundredth as needed. Use a comma to separate answers as needed.) The maximum volume is (2) (Round to the nearest hundredth as needed.) (1) O in.. (2) O in." O in. in. O in. O in. . 9. A waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 26 yd" of debris. Find the dimensions of the dumpster that will minimize its surface area. Write the surface area formula in terms of the width, x. Assume the dumpster has an open top. SA = The width of the dumpster is (1) The length of the dumpster is (2) The height of the dumpster is (3) [Round to the nearest hundredth as needed.) (1) O yd. (2) O yd. (3) O yd. O yd3 O yd O yd? O yd3