A state’s legislature has R representatives. The state is sectioned into s districts, where District j has a population

A state’s legislature has R representatives. The state is sectioned into s districts, where District j has a population p j and s < r.=”” under=”” strictly=”” proportional=”” representation.=”” district=”” j=”” would=””>representatives; this allocation is not feasible, however, because rj may not be integer-valued. The objective is to allocate y j representatives to District j for j = 1, 2, . . . ,s, so as to minimize, over all the districts, the maximum difference between y j and rj ; that is, minimize [maximum (|y1 − r1|, |y2 − r2|, . . . , |ys − rs |)].

a) Formulate the model in terms of a dynamic-programming recursion.

b) Apply your method to the data R = 4, s = 3, and r1 = 0.4, r2 = 2.4, and r3 = 1.2.

c) Discuss whether the solution seems reasonable, given the context of the problem.


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