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Case Problem 1 Production Strategy Big Train Cars Corporation (BTC), manufactures railroad cars. They develop two different lengths of freight cars, a 50' and a 60' model. They believe that the quality and longevity of their cars far surpass their competitors. Being that the demand far exceeds the supply, they believe that all of the freight cars that they build will sell quickly. However, each freight car requires a different amount of each resource to produce. The 50 model can haul up to 75 tons of goods. The 60' model can haul up to 120 tons of goods. Each 50' model requires 40 tons of steel to build, and each 60' model requires 50 tons. Each freight car will also require two sliding doors for each car. The cost per ton of steel is $700. Each 50' model requires 200 hours of building time and 50 hours of finishing time. Each 60 model requires 250 hours of building time and 75 hours of finishing time. Each of the 50' models will require 10 wheels, while the 60' models will require 14 wheels. For the next production period, management estimates that there will be 5000 tons of steel available to be used. There are 300 slide doors available for use costing $1200 each. There are 30,000 hours of building time and 6800 hours of finishing time available. Current labor costs are $25 per hour for building and $20 per hour for finishing The market in which the two freight cars will be sold suggest a retail price of $160,000 for the 50' model and $200,000 for the 60' model. Additionally, there are 1500 wheels available at a price of $150 per wheel. Each car can be painted in red, blue, or green. Because of the current trends in the railroad industry using larger cars, the manager of BTC requires that the company build at least 30% of their cars at a length of 60| Managerial Report Analyze the production problem at Big Train Cars Corporation, and prepare a report presenting your findings and recommendations. Include (but do not limit your discussion to) a consideration of the following items. Round your answers to whole numbers if needed 1. What is the recommended number of 50' and 60' cars to produce if the company's goal is to maximize profit? 2. What is the profit gained from the sale of all of the cars? 3. If an additional 50 tons of steel was made available for $15,000, would it be worth your while to purchase it? Justify your answer. 4. How many hours were used for building time? 5. How much could you raise the price of the 50' freight car before the optimal solution would change? 6. Would the optimal solution change if the goal was to maximize the amount of capacity for the goods? Also, what would be the profit under this decision? Include a copy of your linear programming model with your objective functions and all constraints written ont in an appendix of your report