Suppose that four apartment buildings A, B, C, and D are located along a highway at the points 0,1, 3, and 5, as shown in the following figure. Suppose also that 10 percent of the employees of a certain company live in building A, 20 percent live in B, 30 percent live in C, and 40 percent live in D.
(a) Where should the company build its new office in order to minimize the total distance that its employees must travel?
(b) Where should the company build its new office in order to minimize the sum of the squared distances that its employees must travel?