Question

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 BFI-patented technology that provides the user with an extremely wide range of motion capability for each type of exercise performed. Until now, such capabilities have been available only on expensive weight machines used primarily by physical therapists. At a recent trade show, demonstrations of the machines resulted in significant dealer interest. In fact, the number of orders that BFI received at the trade show far exceeded its manufacturing capabilities for the current production period. As a result, management decided to begin production of the two machines. The two machines, which BFI named the BodyPlus 100 and the BodyPlus 200, require different amounts of resources to produce.

The BodyPlus 100 consists of a frame unit, a press station, and a pec-dec station. Each frame produced uses 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 time and 1 hour of painting and finishing time, and each pec-dec station uses 2 hours of machining and welding time and 2 hours of painting and finishing time. In addition, 2 hours are spent assembling, testing, and packaging each BodyPlus 100.

The BodyPlus 200 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 4 hours of painting and finishing time. Each press station requires 3 hours of machining and welding time and 2 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, and each leg-press station requires 2 hours of machining and welding time and 2 hours of painting and finishing time. In addition, 2 hours are spent assembling, testing, and packaging each BodyPlus 200.

For the next production period, management estimates that 500 hours of machining and welding time; 350 hours of painting and finishing time; and 120 hours of assembly, testing, and packaging time will be available.

The net retail price of the BodyPlus 100 and the BodyPlus 200 are $350 and $445,respectively. Although some flexibility may be available to BFI because of the unique capabilities of the new machines. Authorized BFI dealers can purchase machines for 70% of the suggested retail price. BFI’s president believes that the unique capabilities of the BodyPlus 200 can help position BFI as one of the leaders in high-end exercise equipment. Consequently, she states that the number of units of the BodyPlus 200 produced must be at least 35% of the total production of BodyPlus 100.

Analyze the production problem at Better Fitness, Inc., and prepare a report for BFI’s president presenting your findings and recommendations. The report should include the following items:

• The recommended number of BodyPlus 100 and BodyPlus 200 machines (In other words, find the optimal level of production for BodyPlus 100 and BodyPlus 200 using linear programming model).
  • Objective function: Total profit
  • BodyPlus 200 requirement constraint
  • Non-negativity constraint
  • Time Constraint:
    • Machining & Welding
    • Painting & Finishing
    • Assembly, Test, and Packaging
• The effect on profits of the requirement that the number of units of the BodyPlus 200 produced must be at least 25% of the total production of BodyPlus 100. where efforts should be expended in order to increase contribution to profits
• Include a copy of your linear programming model

To the expert that requested additional information. There is not more information. This is the question in its entirety. This is for a quantitative business modeling class in which we need to use excel’s solver tool. Please provide step by step instructions.

Answer 1

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