Wednesday, July 27, 2016

Highway Billboard Problem

Sup­pose you’re man­ag­ing con­struc­tion of bill­boards on the Rocky & Bull­win­kle Memo­r­ial High­way, a heav­ily trav­eled stretch of road that runs west-east for M miles. The pos­si­ble sites for bill­boards are given by num­bers x1 < x2 < · · · < xn, each in the inter­val [0, M], spec­i­fy­ing their posi­tion in miles mea­sured from the west­ern end of the road. If you place a bill­board at posi­tion xi , you receive a rev­enue of ri > 0.

Reg­u­la­tions imposed by the High­way Depart­ment require that no two bill­boards be within five miles or less of each other. You’d like to place bill­boards at a sub­set of the sites so as to max­i­mize your total rev­enue, sub­ject to this restriction.

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