Better Fitness, Inc. (BFI), manufactures exercise equipment atits plant in Freeport, Long Island. It recently designed twouniversal weight machines for the home exercise market. Bothmachines use BFI-patented technology that provides the user with anextremely wide range of motion capability for each type of exerciseperformed. Until now, such capabilities have been available only onexpensive weight machines used primarily by physical therapists. Ata recent trade show, demonstrations of the machines resulted insignificant dealer interest. In fact, the number of orders that BFIreceived at the trade show far exceeded its manufacturingcapabilities for the current production period. As a result,management decided to begin production of the two machines. The twomachines, 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, anda pec-dec station. Each frame produced uses 4 hours of machiningand welding time and 2 hours of painting and finishing time. Eachpress station requires 2 hours of machining and welding time and 1hour of painting and finishing time, and each pec-dec station uses2 hours of machining and welding time and 2 hours of painting andfinishing 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, apec-dec station, and a leg- press station. Each frame produced uses5 hours of machining and welding time and 4 hours of painting andfinishing time. Each press station requires 3 hours of machiningand welding time and 2 hours of painting and finishing time, eachpec-dec station uses 2 hours of machining and welding time and 2hours of painting and finishing time, and each leg-press stationrequires 2 hours of machining and welding time and 2 hours ofpainting and finishing time. In addition, 2 hours are spentassembling, testing, and packaging each BodyPlus 200.
For the next production period, management estimates that 500hours of machining and welding time; 350 hours of painting andfinishing time; and 120 hours of assembly, testing, and packagingtime will be available.
The net retail price of the BodyPlus 100 and the BodyPlus 200are $350 and $445, respectively. Although some flexibility may beavailable to BFI because of the unique capabilities of the newmachines. Authorized BFI dealers can purchase machines for 70% ofthe suggested retail price. BFI’s president believes that theunique capabilities of the BodyPlus 200 can help position BFI asone of the leaders in high-end exercise equipment.Consequently, she states that the number of units ofthe BodyPlus 200 produced must be at least 35% of the totalproduction of BodyPlus 100.
Analyze the production problem at Better Fitness, Inc.,and prepare a report for BFI’s president presenting your findingsand recommendations. The report should include thefollowing items:
The recommended number of BodyPlus 100 and BodyPlus 200 machines(In other words, find the optimal level of production for BodyPlus100 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 ofunits of the BodyPlus 200 produced must be at least 25% of thetotal production of BodyPlus 100. where efforts should be expendedin order to increase contribution to profits
Include a copy of your linear programming model
