1. ProKick manufactures soccer balls at three factories (labeled A, B, and C), and ships them to stores in California, Arizona, New Mexico, and Texas. Each store has a demand that must be satisfied, each factory has a maximum possible output, and there are different shipping costs (per soccer ball) between factory and store, as tabulated below: (a) Formulate a minimum cost transportation problem to satisfy store demand while minimizing shipping costs. Make sure to define your variables and provide a brief descriptive label for each functional constraint. Ignore integrality. (b) Solve the model you created in part (a) using MATLAB or other software. (c) Suppose ProKick wishes to open a new factory (D), with the below per-ball shipping costs and maximum factory output. Modify your model from part (a) to include this new factory. Solve this model using MATLAB or other software. How is the optimal solution to this problem different from the optimal solution found in part (b)? 1 (d) (Continuation of part c) Suppose there are also production costs for making soccer balls (in addition to shipping them). These costs per ball vary by factory as follows: Modify your model from part (c) to minimize total costs = shipping costs + production costs. Solve this model using MATLAB or other software. How is the optimal solution to this problem (in terms of open and closed factories) different from the optimal solution found in part (c)? 1. ProKick manufactures soccer balls at three factories (labeled A, B, and C), and ships them to stores in California, Arizona, New Mexico, and Texas. Each store has a demand that must be satisfied, each factory has a maximum possible output, and there are different shipping costs (per soccer ball) between factory and store, as tabulated below: (a) Formulate a minimum cost transportation problem to satisfy store demand while minimizing shipping costs. Make sure to define your variables and provide a brief descriptive label for each functional constraint. Ignore integrality. (b) Solve the model you created in part (a) using MATLAB or other software. (c) Suppose ProKick wishes to open a new factory (D), with the below per-ball shipping costs and maximum factory output. Modify your model from part (a) to include this new factory. Solve this model using MATLAB or other software. How is the optimal solution to this problem different from the optimal solution found in part (b)? 1 (d) (Continuation of part c) Suppose there are also production costs for making soccer balls (in addition to shipping them). These costs per ball vary by factory as follows: Modify your model from part (c) to minimize total costs = shipping costs + production costs. Solve this model using MATLAB or other software. How is the optimal solution to this problem (in terms of open and closed factories) different from the optimal solution found in part (c)
