Assume a continuum of consumers are uniformly distributed along the in- terval [0, 1]. A social planner chooses the placements of three "shops". Con- sumers have linear transportation costs and visit the shop that is closest to their location. Each consumer incurs a cost of 1 if she or he travels a distance 1. Please note that to obtain full marks, you need to provide detailed solutions and show your work. (a) [10 points] Derive the locations a*, b* and c* of the three shops that minimize aggregate transportation cost T(a, b, c). What is the corresponding minimum cost? (b) [10 points] Suppose now that two shops already exist: one at location 0 and the other at location 5/6. The social planner is choosing where to place another (the third) shop but can also relocate the existing two shops. The cost of relocating a shop depends on the distance required: if a shop needs to be "moved" distance d, then the relocation cost is d. What are the optimal locations 2*, y* and 2* of the three shops that minimize aggregate transportation and relocation cost T(x, y, z). What is the corresponding minimum cost?