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 Body- plus 100 and the BodyPlus 200, require different amounts of resources to produce.
Managerial Report
Analyze the production problem at Better Fitness, Inc., and prepare a report for BFI’s president presenting your findings and recommendations. Include (but do not limit your discussion to) a consideration of the following items:
1. The recommended number of BodyPlus 100 and BodyPlus 200 machines to produce
2. 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
3. Where efforts should be expended in order to increase contribution to profits Include a copy of your linear programming model and graphical solution in an appendix to your report.

Answer 1

1. Let       BP100 = the number of BodyPlus 100 machines produced

     BP200 = the number of BodyPlus 200 machines produced

 

Max	371BP100	+	461BP200
s.t.
	8BP100	+	12BP200	≤	600	Machining and Welding
	5BP100	+	10BP200	≤	450	Painting and Finishing
	2BP100	+	2BP200	≤	140	Assembly, Test, and Packaging
	-0.25BP100	+	0.75BP200	≥	0	BodyPlus 200 Requirement

 

BP100, BP200 ≥ 0

 

 

 

Optimal solution: BP100 = 50, BP200 = 50/3, profit = $26,233.33. If the optimal solution is rounded to BP100 = 50, BP200 = 16.67, the value of the optimal solution will differ from the value shown. The value we show for the optimal solution is the same as the value that will be obtained if the problem is solved using a linear programming software package such as The Management Scientist.

 

2. In the short run the requirement reduces profits.  For instance, if the requirement were reduced to at least 24% of total production, the new optimal solution is BP100 = 1425/28, BP200 = 225/14, with a total profit of $26,290.18; thus, total profits would increase by $56.85.  Note: If the optimal solution is rounded to BP100 = 50.89, BP200 = 16.07, the value of the optimal solution will differ from the value shown.  The value we show for the optimal solution is the same as the value that will be obtained if the problem is solved using a linear programming software package such as The Management Scientist.

 

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. Since the optimal solution uses all of the available machining and welding time, management should try to obtain additional hours of this resource.