Complete Five Problems Where You Analyze Common Approaches

Complete Five Problems In Which You Analyze Common Approaches To Deter

Complete five problems in which you analyze common approaches to determining product or service quantities based on financials, contribution to profit based on a specific price and volume, product reliability, and quality control. This assessment explores the quality tools companies use to monitor, control, and analyze their products or services. Most businesses in today's economy must invest in quality to survive. Experts on quality have consistently shown that investing in programs and processes to ensure high quality does pay off. By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria: Competency 2: Apply the tools and technology used in operations management. Apply operations management tools associated with determining a breakeven analysis. Apply operations management tools associated with determining contribution to profit. Apply operations management tools associated with determining reliability based on a product with subcomponents used in series. Apply operations management tools associated with determining reliability based on a product with subcomponents used in parallel and in series. Apply operations management tools associated with determining control limits.

Scenario Suppose that you were recently hired as the operations manager for ABC Manufacturing, a small manufacturing company founded two years ago. The company has been reasonably successful since it was founded, but has recently been experiencing several production issues. You were hired to recommend and implement improvements to get the company back on track. Problems Complete the following problems based on the ABC Manufacturing scenario above. For each question, briefly describe the operations management issue and describe how you would approach an analysis, then provide answers to the algebraic equations.

Question 1. ABC Manufacturing is unsure of the ideal price to quote for one of their products, a pump. ABC's president has asked you to do a break even analysis for the pump, and to recommend the optimal price. The fixed costs (FC) associated with manufacturing this particular product are $100,000, and the variable costs (VC) are $50 per unit. ABC's president is considering a selling price (P) for this product of $100. The president wants to know how many units have to be sold in order to break even (BEU). Analyze this operations management issue. Provide the algebraic equation (using BEU, FC, P, and VC as variables) for the breakeven analysis. Calculate and provide the numeric breakeven value.

Question 2. ABC's president believes there is substantial competition for this type of pump, and that price is a significant factor in potential customer's purchase decision. He estimates that the company will sell 3,600 pumps (unit volume or UV) if they are priced at $100, and will sell 2,900 pumps if they are priced at $110. He wants to know what contribution to profit (CP) would result from each of those two selling prices, and thus which is the better price. Analyze this operations management issue. Provide the algebraic equation (using CP, UV, P, and VC as variables) for this analysis. Calculate and provide the numeric contribution to profit (in dollars) for each of the two price points.

Question 3. Another issue ABC is facing is reliability of their products, in part because they are manufacturing increasingly complex products. One such product is designed and manufactured with five different subassemblies combined in series. It was determined through testing that those subassemblies have reliabilities, which are R1, R2, R3, R4, and R5; of .997, .998, .995, .999, and .990, respectively. ABC's president has asked you what the reliability of the overall product (RP) is, given those subassembly reliabilities utilized in series. Analyze this operations management issue. Provide the algebraic equation (using RP, R1, R2, R3, R4, and R5 as variables) for this analysis. Calculate and provide the overall product reliability, given those subassemblies utilized in series.

Question 4. ABC's president has also asked you what the overall reliability of a different product (RP) is. That product has four subcomponents (SC1, SC2, SC3, and SC4). The components are organized as SC1, followed by SC2 in parallel with SC3, which are then both followed by SC4. Their respective reliabilities are SC1R=.97, SC2R=.98, SC3R=.95, and SC4R=.93. Analyze this operations management issue. Provide the algebraic equation (using RP, SC1R, SC2R, SC3R, and SC4R as variables) for this analysis. Calculate and provide the overall product reliability given those subassemblies.

Question 5. ABC Manufacturing is also concerned about the quality of its manufacturing processes. One of the products the company sells is a bottle of liquid lubricant associated with the pump product line. ABC's president is familiar with the operations management concept of control limits (determining an upper and lower numerical threshold such that a process is considered in control as long as it stays within those limits). The president has asked you to take samples of the amount of liquid in those bottles and determine the upper control limit (UCL) and lower control limit (LCL) of three standard deviations. He told you that, based on previous testing, the standard deviation (SD) for this process is 0.035. You took sample measurements of the volume of liquid in the bottles, done at different times of the day, and this produced the data in the Sample Measurements Table:

Time | Volume of Liquid in Bottles of Lubricant (Ounces)

8:00am | 30.039

9:00am | 30.041

10:00am | 29.981

11:00am | 30.011

12:00pm | 30.001

1:00pm | 29.972

2:00pm | 30.083

3:00pm | 29.984

4:00pm | 29.995

5:00pm | 29.98

The mean (M) of these samples is 30.006. Analyze this operations management issue. Provide the algebraic equation for the UCL and for the LCL, using UCL, LCL, M, and SD as variables. Calculate and provide the numerical UCL and LCL values.

Additional Requirements Written communication should be free of errors that detract from the overall message. APA formatting: Any references and citations should be formatted according to APA (6th edition) style and formatting. Font and font size: Times New Roman, 12-point.>

Paper For Above instruction

The comprehensive analysis of operations management tools as demonstrated through the five outlined problems provides critical insights into effective decision-making in manufacturing settings. This paper explores each problem's operational challenge and discusses the mathematical models used for analysis, supported by calculations to inform strategic choices.

Question 1: Breakeven Analysis for Pump Pricing

The first issue involves determining the optimal selling price to achieve breakeven sales volume for a pump product at ABC Manufacturing. The key challenge is to identify the unit sales required to cover fixed and variable costs at a given price point.

The algebraic equation for breakeven volume (BEU) is derived by setting total revenue equal to total costs:

BEU = FC / (P - VC)

Given fixed costs (FC) = $100,000, variable costs (VC) = $50, and proposed price (P) = $100, the calculation is:

BEU = 100,000 / (100 - 50) = 100,000 / 50 = 2000 units

Thus, ABC Manufacturing needs to sell at least 2,000 pumps at $100 to break even.

Question 2: Contribution to Profit at Different Price Points

The second issue addresses how pricing impacts contribution to profit (CP) based on demand estimates at different prices. Contribution to profit is calculated as:

CP = (P - VC) * UV

At a selling price of $100 with projected sales of 3,600 units:

CP = (100 - 50)  3,600 = 50  3,600 = $180,000

At a selling price of $110 with an estimated sales volume of 2,900 units:

CP = (110 - 50)  2,900 = 60  2,900 = $174,000

The analysis shows that pricing at $100 yields higher contribution to profit, despite the lower price, primarily due to higher projected sales volume.

Question 3: Reliability of Products in Series

Product reliability is essential for quality assurance; when subcomponents are arranged in series, the overall system reliability (RP) is the product of individual reliabilities:

RP = R1  R2  R3  R4  R5

Using the given reliabilities:

RP = 0.997  0.998  0.995  0.999  0.990 ≈ 0.969

The overall reliability of this complex product is approximately 96.9%, indicating a high standard but highlighting potential areas for improvement.

Question 4: Reliability of a Parallel-Series Product Configuration

In a configuration where subcomponents are arranged with some in parallel, the overall reliability must account for both series and parallel arrangements. For components in series, reliabilities multiply; for components in parallel, the reliability is 1 minus the product of their failure probabilities.

Given:

• SC1R = 0.97
• SC2R = 0.98
• SC3R = 0.95
• SC4R = 0.93

The combined reliability of SC2 and SC3 in parallel (SC23R) is:

SC23R = 1 - [(1 - 0.98)  (1 - 0.95)] = 1 - (0.02  0.05) = 1 - 0.001 = 0.999

Then, the overall reliability (RP) is:

RP = SC1R  SC23R  SC4R = 0.97  0.999  0.93 ≈ 0.899

Thus, the overall reliability is approximately 89.9%, indicating robust performance with some room for improvement particularly in the last subcomponent.

Question 5: Control Limits for Liquid Volume in Bottles

Control limits in quality management define the acceptable variation in a process. For the liquid volume in bottles, the upper control limit (UCL) and lower control limit (LCL) are calculated using the mean (M), standard deviation (SD), and the number of standard deviations (typically 3) for in-control processes:

UCL = M + 3 * SD
LCL = M - 3 * SD

Given:

• M = 30.006 ounces
• SD = 0.035 ounces

Calculations:

UCL = 30.006 + 3 * 0.035 = 30.006 + 0.105 = 30.111 ounces
LCL = 30.006 - 0.105 = 29.901 ounces

The process is considered in statistical control as long as the bottle volumes stay within approximately 29.901 to 30.111 ounces.

Conclusion

The detailed analysis demonstrates the significance of applying quantitative tools such as breakeven analysis, contribution calculations, reliability modeling, and control charts in operations management. These tools facilitate data-driven decisions, enhance process reliability, and optimize product quality—cornerstones for competitive advantage in manufacturing.

References

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