Better Fitness, Inc. (BFI), manufactures exercise equipment at its plant in Freeport, Lon Island. It recently designed two universal weight machines for the home exercise market. Both machines use BFI-patented technology that provides the used 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 primarily used 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 the 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. Each pec-dec 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 100. The raw material costs are $450 for each frame, $300 for each press station, and $250 for each pec-dec station. Packaging costs are estimated to be $50 per unit.

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 requires 2 hours of machining and welding time, and 2 hours of painting and finishing time. 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. The raw material costs are $650 for each frame, $400 for each press station, $250 for each pec-dec station, and $200 for each leg press station. Packaging costs are estimated to be $75 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 labor costs are $20 per hour for machining and welding time, $15 per hour for painting and finishing time, and $12 for assembly, testing, and packaging time. The market in which these two machines must compete suggests a retail price of $2400 for the BodyPlus 100 and $3500 for the BodyPlus 200, although some flexibility may be available to BFI because of the unique capabilities of the new machines. Authorized dealers can purchase machines for 70% of the suggested retail price.

BFIs 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, he has states that the number of units of the BodyPlus 200 produced must be at least 25% of the total production.

Statement of Purpose of the Report.

What is the purpose of this report? What problem is being addressed?

Presentation of data.

Since this comes from the handout, data does not need to be collected. But what is the factual information given in this problem. What are the uncontrollable inputs? What are the controllable inputs?

Compose problem statement into a comprehensive mathematical model.

Give the linear program you have developed. Explain the objective function and the constraints. Show how these address the purpose of the report.

Propose and justify optimal solution in the context of the problem statement.

Provide the complete solution to the linear program. Note that this will be the response to question #1 of the Case Problem. Include Excel output to support answer.

1) What is the recommended number of BodyPlus 100 and BodyPlus 200 machines to produce to maximize the profit?

Perform sensitivity analysis of the optimal solution.Questions #2, and #3 of the Case Problem each consider alternatives to the original problem. Respond to each of these questions with a short analysis of the differences and the implications of these differences in terms of the problem statement. For which of these does the solution change? Include Excel outputs to support answers.

2) How does the requirement that the number of units of BodyPlus 200 produced be at least 25% of the total production affect profits?

3) Where should efforts be expended in order to increase profits? Give at least one specific example, explain, and justify.

Keep in mind what values we can change (controllable) and which values we cannot change (uncontrollable).

Communicate the solution to an appropriate audience.

This report is for the President of the company. Make sure your explanations are appropriate, professional, and do a good job explaining the outcomes to someone who may not be mathematically minded. This will need to be maintained throughout the entire paper.