# Manufacturing decisions | Management homework help

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 (refer to the Question 3 Flowchart). 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 (refer to the Question 4 Diagram). 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 (in case that somehow impacted the volume), and this produced the data in the Sample Measurements Table below:

Sample Measurements TableTimeVolume of Liquid in Bottles of Lubricant (in Ounces)8:00am30.039:00am30.0410:00am29.9811:00am30.0112:00pm30.001:00pm29.972:00pm30.083:00pm29.984:00pm29.995:00pm29.98Mean (M)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 ULC and LCL values.

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