Q) A discount store chain wants to build a new superstore in an area in Melbourne near four small towns with populations between 10,000 and 40,000. The coordinates (in miles) of these four towns and the market population in each are as follows: Coordinates Carlton St Kilda Ballarat Frankston 12 18 30 32 20 12 8 25 Population 18,000 17,000 10,300 10,000 a) Determine the best site using the center-of-gravity technique. b) Suppose the store is limited to two possible sites for locating a new superstore. The coordinates (in miles) of these two potential sites are site 1 (10, 30) and site 2 (20, 10). Using the load-distance technique, determine the best site for the new super store. c) Plot the four small towns and the proposed new distribution centers according to center of gravity method and load-distance method on a grid map. Give your own opinion about it.

William Green, vice president of manufacturing for computer products (CPC), and his staff are studying three midwestern alternative locations for a new production facility for producing high-resolution scanners. His staff analysts predict that the scanners will be a growing market over the next ten years, and the analyst's group shares marketing's enthusiasm for planning facilities for producing this new product line. The analysts have developed these estimates for the three locations; In what range of production volume would each of the locations be preferred (at the minimum cost)?     Variable cost locations Annual Fixed costs per scanner Cleveland, Ohio $390,000 $34 South Bend, Indiana $360,000 $37 Grand Rapids, Michigan $310,000 $40

The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 350x1 + 425x2 + 425x3+ 465x4 + 485x5 + 365x6 s.t. x1 + x2 + x5 + X6 2 1 (Residence Hall A constraint) x1 + x2 + X3 2 1 {Residence Hall B constraint) X4 + X5 + X6 2 1(Science building constraint) X1 + X4 + X5 2 1{Music building constraint} x2 + x3 + X4 2 1{Math building constraint} x3 + X4 + X5 2 1{Business building constraint} x2 + x5 + X6 2 1{Auditorium…

1. Using the center-of-gravity method, compute the centralized coordinates among the following locations, which are indicated via black cells with white text in LOCATION.xlsx: 7,1 10,1 4,2 2,5 6,6 9,6 2,8 6,10 2. Using the weighted average center-of-gravity, which accounts for quantities to be shipped from locations, compute the centralized coordinates among the following locations: 7,1 10,1 4,2 2,5 6,6 9,6 2,8 6,10 *Quantities to be shipped are listed within the existing locations (i.e. Location 7,1 ships 17 units) in LOCATION.xlsx