At a recent trade show, demonstrations of the machines resulted in significant dealer interest. As a result, management decided to begin production of the two machines. The two machines, which CH has named the Gym100 and the Gym200, require different amounts of resources to produce. The Gym100 consists of a frame unit, a press station and a pec-dec station. Each frame produced uses 5 hours of machining and welding time and 2 hours of painting and finishing time. Each press station requires 1 hour of machining and welding time and 1 hour of painting and finishing time. Each pec-dec station uses 1 hours of machining and welding time and 2 hours of painting and finishing time. In addition, 3 hours are spent assembling, testing and packaging each Gym100. The raw material costs are 500 for each frame, 400 for each press station and 350 for each pec-dec station; packaging costs are estimated to be 25 per unit. The Gym200 consists of a frame unit, a press station, a pec-dec station and a leg-press station. Each frame produced uses 5 hours of machining and welding time and 3 hours of painting and finishing time. Each press station requires 2 hours of machining and welding time and 3 hours of painting and finishing time. Each pec-dec station uses 2 hours of machining and welding time and 2 hours of painting and finishing time. Each leg-press station requires 3 hours of machining and welding time and 1 hour of painting and finishing time. In addition, 2 hours are spent assembling, testing and packaging each Gym200. The raw material costs are 790 for each frame, 500 for each press station, 390 for each pec-dec station and 300 for each leg-press station; packaging costs are estimated to be 25 per unit. For the next production period, management estimates that 600 hours of machining and welding time, 450 hours of painting and finishing time and 140 hours of assembly, testing and packaging time will be available. Current labour 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 in which the two machines must compete suggests a retail price of 2750 for the Gym100 and 3750 for the Gym200, although some flexibility may be available to CH because of the unique capabilities of the new machines. Authorised CH dealers can purchase machines for 70% of the suggested retail price. CH does not sell to the public only to authorised CH dealers! CH's managing director believes that the unique capabilities of the Gym200 can help position CH as one of the leaders in high-end exercise equipment. Consequently, he has stated that the number of units of the Gym200 produced must be at least 30% of the total production. You are required: 1. to formulate (objective function and constraints) the brief as a Linear Programming (LP) problem 2. solve the LP problem graphically 3. solve the LP problem using The Management Scientist software 4. apply sensitivity analysis to analyse the production problem at Complete Health Ltd 5. prepare a structured Management Report for CH's managing director presenting your findings and recommendations, and discuss your findings in relation to the problem. 6. Report should include (but do not limit your discussion to) a consideration of the following items: o Calculation for formulation, graphical solution and The Management Scientist output. o The recommended number of Gym100 and Gym200 machines to produce and total profit. o Where efforts should be expended in order to increase profits. (Sensitivity Analysis with examples) o The effect on profits of the requirement that the number of units of the Gym200 produced must be at least 25% of the total production. Where efforts should be expended in order to increase profits. (Sensitivity Analysis