Better Fitness Inc. (BFI), manufactures exercise equipment at its plant in Melbourne. It recently designed two universal weight machines for the home exercise market. 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. 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 hours of painting and finishing time, and each pec-dec station uses 2 hours of machining and welding time and 2 hours of paining and finishing time. In addition 2 hours are spend 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 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. 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 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 $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.

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

Assessment Tasks:

LetBP100 = the number of BodyPlus 100 machines produced

BP200 = the number of BodyPlus 200 machines produced

Answer all questions below.

1. Define the objective function and constraints for this case.
2. Graphically show optimal solution and feasible area for the case.
3. If management really believes that the BodyPlus 200 can help position BFI as one of the leader's in high-end exercise equipment, the constraint requiring that the number of units of the BodyPlus 200 produced be at least 25% of total production should not be changed. Discuss why?