please please help. operations research, please write in a case report format:)

Better Fitness, Inc. (BFI) manufactures exercise equipment at its plant in Freeport, Long Island. It recently designed two universal weight machines for the home exercise market. Both machines use BFIpatented technology that provides the user with an extremely wide range of motion for each type of exercise. At a recent trade show, demonstrations resulted in significant dealer interest. The two machines, which BFI named the BodyPlus 100 (BP100) and the BodyPlus 200 (BP200), require different amounts of resources to produce. The BP100 consists of a frame, a press station, and a pec-dec station. Bach frame requires 4 hours of machining and welding time and 2 hours of painting and finishing time. Each press station requires 2 hours of machining and welding and 1 hour of painting and finishing time. Each pec-dec station requires 2 hours of machining and welding and 2 hours of painting and finishing time. The BP100 also requires 2 hours of assembly, testing, and packaging. The part costs for the BP100 are $450 for a frame, $300 for each press station, and $250 for eachpec-dec. Packaging costs are $50 per unit. The BP200 consists of a frame, a press station, a pec-dec station, and a leg-press station. Each frame requires 5 hours of machining and welding time and 4 hours of painting and finishing time. Each press station requires 3 hours of machining and welding and 2 hours of painting and finishing time. Each pecdec station requires 2 hours of machining and welding and 2 hours of painting and finishing time. The BP200 also requires 2 hours of assembly, testing, and packaging. The part costs for the BP200 are \$650 for a frame, \$400 for each press station, and \$250 for each pec-dec station, and $200 for cach leg-press station. Packaging costs are $75 per unit. The part costs for the BP 200 are $650 for a frame, $400 for each press station, and $250 for each pec-dec station, and $200 for each leg-press station. Packaging costs are $75 per unit. For the next production period, management estimates that 600 hours of machining and packaging time will be available, 450 hours of painting and finishing time and 132 hours of assembly, testing, and packaging time. Current labor costs are $20 per hour for machining and welding time; $15 per hour for painting and finishing time; and $12 per hour for assembly, testing, and packaging time. The market suggests the BP100 can be sold for a retail price of $2400 and the BP200 can be sold for $3500. BFI sells to authorized dealers at 70% of retail price. BFI's president believes that the unique capabilities of the BP200 can help position BFI as one of the leaders in the high-end exercise equipment. Consequently, she states that the number of units of the BP200 produced must be at least 25% of the total production of machines. The table below summarizes the revenue and cost information from above. Revenue and Cost Elements for the BP100 and BP200 Managerial Report Analyze the production problem for BFI Inc. and prepare a report for BFI's president presenting your findings and recommendations. Include (but do not limit your discussion to) a consideration of the following items. Managerial Report Analyze the production problem for BFI Inc. and prepare a report for BFI's president presenting your findings and recommendations. Include (but do not limit your discussion to) a consideration of the following items. 1. What is the profit per unit for each BP100 and BP200? 2. What is the recommended number of BP 100 and BP 200 machines BFI should produce in order to maximize profit? 3. Would it be worthwhile to hire an additional worker to do machining and welding if that worher could devote 10 hours to production of BP100 and BP200? Include a copy of the mathematical formulation of this linear programming model along with a copy of your Excel spreadsheet setup with solution in an appendix to your report