Please answer ALL questions and provide ALL workings.

a. A manufacturing company preparing to build a new plant is considering three potential locations for it. The fixed and variable costs for the three aliernative locations are gresented in the table below 1. Indicate over what range, each of the alternatives A, B, C is the low-cost cheice. [10 marks] b. A langer and more modern post office is to be constructed at a new location in 5 ally Spring Georgia. Growing suburbs caused a shift in the population density from where it was 30 years ago when the current facility was bulit. Andy Browne, the postmaster asked his assistants to draw a grid map of the seven points where mail is picked up and delivered in bulk. The coordinates and trips per day to and from the seven mail source points and the current main post office are shown in the table bulaw. i. Cakulate the ecntte of gravity as a possible location fot the new facility. [10 marks] c. A clothing thain is considering two differnt locatices for a new metsil vetlet. The of ganization has identified the four factoes listed in the following table as the basb for evaluation and it has assigned weights as shown. The manager has rated eakh location an each factoc, on a 100 -point basis Chigher scores are betterl, as ahown under the reppective exhums for Barclay and Chester