A producer of cable modems, routers and other computer peripherals has three manufacturing plants located at Greenville, Stamford and Nicetown. The company has three major distribution centers (DCs) at Chicago, Dallas and New York, from which all demands for its products are fulfilled. A new wireless router is scheduled to be introduced into the market in the near future. This product can be produced at one or more of the existing plants and its estimated annual demand at each DC is shown in the table below. This table also shows the unit transportation costs from the plants to the DCs, the annual output capacity and the allocated annual fixed cost (if this product is produced) for each plant. Unit Transportation Costs To: Annual Output Annual Fixed From: Chicago Dallas New York Capacity (Units) Cost Greenville $1.40 $1.10 $1.30 1,400 $26,000 Stamford $1.25 $1.40 $0.60 1,600 $31,000 Nicetown $1.35 $1.30 $1.45 1,500 $22,000 Annual Demand: 900 800 1,200 (Units) Due to different prevailing local conditions, the unit manufacturing costs are estimated to be $20 at Greenville, $22 at Stamford and $21 at Nicetown. Furthermore, due to competitive market factors, the unit selling prices are to be set at $152, $154 and $151, respectively, for the markets served by the DCs at Chicago, Dallas and New York. (a) In order to find the optimal production allocation and distribution plan for this new product over the upcoming year, formulate (i.e. first, clearly and completely define all decision variables used, then construct the objective function and all constraints in algebraic format) an appropriate linear optimization model, showing all known numerical parameter values. (b) Solve your model in part (a) using Excel/Solver, summarize the results on a separate written or typed page (to be included as a part of your PDF submission) and upload your Excel file via the link provided in BB-Learn.

A producer of cable modems, routers and other computer peripherals has three manufacturing plants located at Greenville, Stamford and Nicetown. The company has three major distribution centers (DCs) at Chicago, Dallas and New York, from which all demands for its products are fulfilled. A new wireless router is scheduled to be introduced into the market in the near future. This product can be produced at one or more of the existing plants and its estimated annual demand at each DC is shown in the table below. This table also shows the unit transportation costs from the plants to the DCs, the annual output capacity and the allocated annual fixed cost (if this product is produced) for each plant. Unit Transportation Costs To: Annual Output From: Chicago Dallas New York Capacity (Units) Greenville $1.40 $1.10 $1.30 1,400 Stamford $1.25 $1.40 $0.60 1,600 Nicetown $1.35 $1.30 $1.45 1,500 Annual Demand: 900 1.200 (Units) Annual Fixed Cost $26,000 $31,000 $22.000 800 Due to different prevailing local conditions, the unit manufacturing costs are estimated to be $20 at Greenville, $22 at Stamford and $21 at Nicetown. Furthermore, due to competitive market factors, the unit selling prices are to be set at $152, $154 and $151, respectively, for the markets served by the DCs at Chicago, Dallas and New York. (a) In order to find the optimal production allocation and distribution plan for this new product over the upcoming year, formulate (i.e. first, clearly and completely define all decision variables used, then construct the objective function and all constraints in algebraic format) an appropriate linear optimization model, showing all known numerical parameter values. (b) Solve your model in part (a) using Excel/Solver, summarize the results on a separate written or typed page (to be included as a part of your PDF submission) and upload your Excel file via the link provided in BB-Learn