2/2014 Manufacturing Application: ( Note: In this project you will use the simplex solver http://www.zweigmedia.com/RealWorld/simplex.html. You should include the input and output from this solver. You can do this by using the copy and paste functions on the computer. ) The Kimble Firefighting Equipment Company makes alarm valves. It has two assembly plants: Plant A in Atlanta and Plant B in Buffalo. Plant A can produce at most 8000 alarm valves and Plant B can produce at most 10000 alarm valves. The cost to produce an alarm valve is $12 at plant A and $18 at Plant B. All the alarm valves produced are shipped to two warehouse locations, one in Pittsburgh and one in Savannah. The grid below shows the distance between these locations: Warehouse I: Pittsburgh Warehouse II: Savannah Plant A: Atlanta 685 miles 248 miles Plant B: Buffalo 215 miles 907 miles The current cost per mile to ship is $0.03. 1. The current cost per mile to ship is $0.03. Calculate the total cost to produce and ship an alarm valve from each location to each warehouse. Put your answers into a matrix like the one above. 2. If the current weekly demand is for at least 9000 alarm valves to be shipped to Warehouse I and at least 6000 alarm valves to be shipped to Warehouse II. Write a linear programming problem to minimize the total cost of production and shipment. Define your variables, state the objective function and list all constraints. 3. Solve you equation using the simplex solver. State your solution in a complete sentence. What is the solution telling you? 4. In winter diesel gas prices increase, does your solution change if the price increased from $0.03 per mile to $0.05 per mile? Rewrite your LP with these new costs and solve. What is the impact on your weekly costs due to this price increase? 5. The plant in Buffalo is old and needs major renovations, while the plant in Atlanta is newer and has room to expand. The company wants to look at the impact of shutting down the Buffalo plant. Using the same costs from problem 4 (with the higher gas prices). First expand the capacity of the Atlanta plant from 8000 to 16000 and take the capacity of the Buffalo plant to 0. Write the new LP and the optimal solution. What would be the cost of shutting down the Buffalo plant? Would you recommend shutting down the Buffalo plant? Use your analysis to justify your answer. 6. Because of Union issues management wants to shut down the Buffalo report. It has produced a report to justify shutting down the Buffalo plant by recommending using rail lines for shipments between Atlanta and Pittsburg which will reduce costs to $0.02 per mile on travel between Atlanta and Pittsburgh. There are not similar cost savings for using rail on the other shipments. How would you use this new information to analyze that their claim is true. Write out any LP you used to answer this question. If the claim is true what is the weekly cost savings? Is the answer the same when gas prices are $0.03 per mile and $0.05 per mile? Would you recommend shutting down the Buffalo plant if this railroad option was available