Yuckdonald’s is considering opening a series of restaurants along Quaint Valley Highway (QVH). The n possible locations are along a straight line, and the distances of these locations from the start of QVH are, in miles and in increasing order, m1; m2,..., mn. The constraints are as follows:
• At each location, Yuckdonald’s may open at most one restaurant. The expected profit from opening a restaurant at location i is pi, where pi > 0 and i = 1,2, ...,n.
• Any two restaurants should be at least k miles apart, where k is a positive integer.
Give an efficient algorithm to compute the maximum expected total profit subject to the given constraints.
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