11 The state of Transylvania consists of three cities with the following populations: city 1, 1.2 million people; city 2, 1.4 million people; city 3, 400,000 people. The Transylvania House of Representatives consists of three representatives.

Given proportional representation, city 1 should have d1 

(

12/3

)  1.2 representatives; city 2 should have d2  1.4 representatives; and city 3 should have d3  0.40 representative. Each city must receive an integral number of representatives, so this is impossible. Transylvania has therefore decided to allocate xi representatives to city i, where the allocation x1, x2, x3 minimizes the maximum discrepancy between the desired and actual number of representatives received by a city. In short, Transylvania must determine x1, x2, and x3 to minimize the largest of the following three numbers: x1  d1, x2  d2, x3  d3. Use dynamic programming to solve Transylvania’s problem.