Solve the associated linear optimization problem using excel (solver).

Better Fitness, Inc. (BFI) manufactures exercise equipment at its Freeport, Long Island plant. It recently designed two weight machines for the home exercise market, the machines use proprietary BFI technology that provides the user with a range of extremely wide movement capacity for each type of exercise performed.

Until now, these capabilities have been available only on expensive weight machines that are primarily used by physical therapists. At a recent trade show, demonstrations of the machines sparked great interest from dealers. In fact, the number of orders BFI received at the trade show far exceeded its manufacturing capabilities for the current production period.

As a result, management decided to start manufacturing of the two machines, which BFI named Body-Plus 100 and BodyPlus 200, and require different amounts of resources to produce. The BodyPlus 100 consists of a frame unit, a press station and a pec-dec. In each structure produced 4 hours of machining and clamping time, and 2 hours of painting and finishing are invested. Each press station requires 2 hours of machining and clamping, and 1 hour of painting and finishing; 2 hours of machining and clamping, and 2 hours of painting and finishing are invested in each pec-dec station. In addition, 2 hours are spent on assembly, testing and the packaging of each BodyPlus 100.

Raw material costs are $ 450 for each structure, $ 300 for each press station and $ 250 for each pec-dec station; packaging is estimated at $ 50 per unit. The BodyPlus 200 consists of a frame unit, a press station, a pecdec and a leg press. In each structure produced, 5 hours of machining and clamping time, and 4 hours of painting and finishing are invested. Each press station requires 3 hours of machining and clamping, and 2 hours of painting and finishing; 2 hours of machining and clamping, and 2 hours of painting and finishing are invested in each pec-dec station; and each leg press station requires 2 hours of machining and clamping, and 2 hours of painting and finishing. In addition, 2 hours are spent on assembling, testing and packaging each BodyPlus 200. Raw material costs are $ 650 for each frame, $ 400 for each press station, $ 250 for each pec-dec station, and $ 300 for each station leg press; packaging is estimated at $ 75 per unit.

For the next production period, management estimates that there will be 600 hours of machining and clamping time, 450 hours of painting and finishing, and 140 hours of assembly. Current labor costs are $ 20 per hour for machining and fastening, $ 15 per hour for painting and finishing, and $ 12 per hour for assembly, testing, and packaging. The market in which the two machines must compete suggests a retail or retail price of $ 2400 for the BodyPlus 100 and $ 3500 for the BodyPlus 200, although there may be flexibility on the part of BFI due to the unique capabilities of the new machines. BFI Authorized Dealers can purchase the machines for 70% of the suggested retail price.

The BFI President believes that the unique capabilities of the BodyPlus 200 can position BFI as one of the leaders in high-quality exercise equipment. Consequently, it was established that the number of BodyPlus 200 units produced should be at least 25% of total production.

Management report Discuss the production problem facing Better Fitness, Inc. and prepare a report for the BFI president outlining your findings and recommendations. Include (but are not limited to) a consideration of the following points: 1. The recommended number of BodyPlus 100 and BodyPlus 200 machines to produce. 2. The effect on earnings of the requirement that the number of BodyPlus 200 units produced be at least 25% of total production. 3. Whether to increase efforts to increase the contribution to profits

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