*14. a. Squares with sides of length x are cut out of each comer of a rectangular piece of cardboard measuring 27 ft by 15 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. b. Suppose that in part (a) the original piece of cardboard is a square with sides of lengths. Find the volume of the largest box that can be formed in this way. a. To find the objective function, express the volume V of the box in terms of x. V= 4x-84x+405x (Type an expression.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation. Use integers or decimals for any numbers in the expression.) The maximum volume of the box is approximately [ (Round to the nearest hundredth as needed.) b. To find the objective function, express the volume V of the box in terms of s and x. V= (Type an expression.) The maximum volume of the box is (Type an expression using s as the variable.) | *13. A hockey player skates on a line that is perpendicular to the goal line. If the line on which he is skating is 8 feet to the left of the center of the hockey goal and if the hockey goal is 6 feet wide, then where (what value of x) should he shoot the puck to maximize the angle 0 on goal (see figure)? (Hint: 0 = - .) Write an objective function in terms of a single independent variable, x. (Type an equation.) The interval of interest for x is (Simplify your answer. Type your answer in interval notation.) The distance that maximizes 0 is x=| (Type an exact answer, using radicals as needed.) (1) O degrees. ft. O ft. (1) x a 6 ft