Case Problem 2 - PRODUCTION STRATEGY
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 therapist.
At a recent trade show, demonstration 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 number of orders that BFI received at the trade show far exceeded its manufacturing capabilities for the current production period. As a result, management decide to begin production of the two machines. The two machines, which BFI has 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, and each pec-dec station uses 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 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 labor 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. Authorized BFI dealers can purchase machines for 70% of the suggested retail prices.
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 least 25% of the total production.
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 produces.
2. The effect on profits of the requirement that the number of units of the BodyPlus 200 produces must be at least 25% of the total production.
3. Where efforts should be expended in order to increase profits.
Include a copy of your linear programming model and graphical solution in an appendix to your report.
27
Pls answer
To analyze the production problem at Better Fitness Inc. (BFI) and prepare a report, we will follow these steps:
Step 1: Define Variables
Identify the variables for the problem. In this case, we need to determine the number of BodyPlus 100 (B1) and BodyPlus 200 (B2) machines to produce.
Step 2: Formulate Objective Function
The objective is to maximize profit. Calculate the profit for each machine and find the total profit.
Profit = (Revenue - Cost)
Revenue = (Number of Machines) * (Wholesale Price)
Cost = (Number of Machines) * (Costs per Machine)
Step 3: Formulate Constraints
Consider the resource constraints in terms of machining and welding time, painting and finishing time, and assembly, testing, and packaging time. Also, account for labor costs and the requirement that at least 25% of the total production must be BodyPlus 200 machines.
Machining and Welding Time: For each machine, the machining and welding time required should not exceed the available time.
4B1 + 5B2 ≤ 600
Painting and Finishing Time: For each machine, the painting and finishing time required should not exceed the available time.
2B1 + 4B2 ≤ 450
Assembly, Testing, and Packaging Time: The total time required for assembly, testing, and packaging should not exceed the available time.
2B1 + 2B2 ≤ 140
Labor Costs: Calculate the total labor costs based on the machines produced.
Labor Costs = (Number of Machines) * (Labor Hours) * (Cost per Hour)
20(4B1 + 5B2) + 15(2B1 + 4B2) + 12(2B1 + 2B2) ≤ Budget
Minimum Requirement for B2 Machines: At least 25% of the total production should be BodyPlus 200 machines.
B2 ≥ 0.25(B1 + B2)
Step 4: Create a Linear Programming Model
Based on the objective function and constraints formulated in Steps 2 and 3, create a linear programming model to maximize profit subject to resource constraints.
Maximize: Profit = (70% * Wholesale Price * Number of Machines) - (Costs per Machine * Number of Machines)
Subject to:
4B1 + 5B2 ≤ 600 (Machining and Welding Time)
2B1 + 4B2 ≤ 450 (Painting and Finishing Time)
2B1 + 2B2 ≤ 140 (Assembly, Testing, and Packaging Time)
20(4B1 + 5B2) + 15(2B1 + 4B2) + 12(2B1 + 2B2) ≤ Budget (Labor Costs)
B2 ≥ 0.25(B1 + B2) (Minimum Requirement for B2)
Step 5: Solve the Linear Programming Model
Use linear programming software or graphical methods to solve the model and find the optimal values for B1 and B2.
Step 6: Analyze Results and Make Recommendations
Evaluate the solution to determine the recommended number of BodyPlus 100 and BodyPlus 200 machines to produce. Consider the effect of the requirement for at least 25% of the total production to be BodyPlus 200 machines and identify areas where efforts should be expended to increase profits.
Present your findings and recommendations in a comprehensive report, including a copy of the linear programming model and graphical solution in an appendix.
To analyze the production problem at Better Fitness, Inc. (BFI), and prepare a report, we need to consider the following items:
1. Recommended number of BodyPlus 100 and BodyPlus 200 machines to produce:
To determine the number of machines to produce, we need to consider the available resources and the demand for each machine. Based on the information provided, we have the following resource constraints:
- Machining and welding time: 600 hours available
- Painting and finishing time: 450 hours available
- Assembly, testing, and packaging time: 140 hours available
In addition, the president of BFI has stated that the number of units of the BodyPlus 200 produced must be at least 25% of the total production.
To solve this problem, we can set up a linear programming model. Let:
- x1 = number of BodyPlus 100 machines produced
- x2 = number of BodyPlus 200 machines produced
The objective function will be to maximize profit:
Maximize Z = 2400x1 + 3500x2
Subject to the following constraints:
4x1 + 5x2 <= 600 (machining and welding time constraint)
2x1 + 3x2 <= 450 (painting and finishing time constraint)
2x1 + 2x2 <= 140 (assembly, testing, and packaging time constraint)
x2 >= 0.25(x1 + x2) (requirement that BodyPlus 200 units be at least 25% of total production)
We can solve this linear programming model using a spreadsheet program like Microsoft Excel or by using linear programming software. The solution will provide the recommended number of BodyPlus 100 and BodyPlus 200 machines to produce.
2. 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:
To determine the effect on profits, we need to compare the profits with and without the requirement. Once we solve the linear programming model, we can calculate the total profit for each scenario and compare the results. By analyzing the difference in profits, we can assess the impact of the 25% requirement on the overall profitability of BFI.
3. Where efforts should be expended to increase profits:
To identify areas for increasing profits, we can focus on different aspects of the production process. Some potential areas to consider are:
- Improving resource utilization: Analyze the resource constraints and identify ways to utilize resources more efficiently. This may involve optimizing production schedules, identifying bottlenecks, or exploring options to increase resource capacity.
- Cost reduction strategies: Examine the costs associated with raw materials, labor, and packaging. Evaluate alternatives for cost reduction, such as negotiating better prices with suppliers, improving production processes, or exploring cheaper packaging solutions.
- Market positioning and pricing: Assess the market demand and competition to determine if pricing adjustments or marketing strategies could increase sales and profitability. Consider factors such as perceived value, uniqueness of the product, and target customer segments.
By analyzing these areas, BFI can identify opportunities for increasing profits and develop strategies to address them. The specific recommendations will depend on the findings from the analysis.
It's important to note that the actual values and calculations may vary based on the specific requirements and constraints of BFI's production process.