Question

You work for the OR state highway agency and must place warning signs along a certain road. Along the way there are n locations at which you may place a sign, at mile posts m1 < m2 < ··· < mn, where each mi is measured from the starting point m1 = 0. The only places you are allowed to place a sign is at one of the given mileposts. In addition, you must place one at locations m1 and mn. Your requirement is to place one every 100 miles, but this may not be possible (depending on the spacing of the mileposts). If you place two consecutive signs x miles apart, the penalty for that placement is (100−x)2. You want to arrange a placement so as to minimize the total penalty - that is, the sum, over all locations, of the penalties. Perform the two steps above to start the process of determining the minimum possible penalty.

Answer 1