Student Name
Capella University
BUS-FPX4014 Operations Management for Competitive Advantage
Prof. Name:
Date
In order to determine how many units need to be sold to break even, it is essential to conduct a break-even analysis. This analysis helps in establishing the ideal price point for the product, in this case, the pump. The key variables are:
The break-even units (BEU) can be calculated using the formula:
[ \text{BEU} = \frac{\text{FC}}{\text{P} – \text{VC}} ]
Substituting the values:
[ \text{BEU} = \frac{100,000}{100 – 50} = \frac{100,000}{50} = 2,000 ]
This means 2,000 units must be sold to break even.
The selling price of a product plays a crucial role in determining the profit margin. While higher prices generally increase the profit per unit, they can also reduce the number of units sold, potentially impacting overall profits. To determine the most profitable price point, a contribution to profit (CP) analysis is essential. The formula for CP is:
[ \text{CP} = (\text{P} – \text{VC}) \times \text{UV} – \text{FC} ]
Where UV represents the units sold. Two price points are considered:
[ \text{CP} = (100 – 50) \times 3,600 – 100,000 = 50 \times 3,600 – 100,000 = 180,000 – 100,000 = 80,000 ]
[ \text{CP} = (110 – 50) \times 2,900 – 100,000 = 60 \times 2,900 – 100,000 = 174,000 – 100,000 = 74,000 ]
From this analysis, it is clear that the more profitable price point is $100 per pump.
Reliability testing focuses on evaluating the functionality and durability of a product. The goal is to assess how long the product will last, thus minimizing the likelihood of defective or returned items. To determine the overall reliability of a product, the following formula is used:
[ \text{RP} = R1 \times R2 \times R3 \times R4 \times R5 ]
Substituting the reliability values for each component:
[ \text{RP} = 0.997 \times 0.998 \times 0.995 \times 0.999 \times 0.990 = 0.979 ]
Thus, the overall reliability of the product is 0.979, indicating high reliability.
When a company manufactures multiple products with various subcomponents, it is important to evaluate the reliability of the entire system, not just individual components. A product’s overall reliability can be calculated by considering the reliability of its subcomponents. The formula used is:
[ \text{RP} = \text{SC1R} \times \left(1 – \left(1 – \text{SC2R}\right) \times \left(1 – \text{SC3R}\right)\right) \times \text{SC4R} ]
Using the following reliability values for the subcomponents:
[ \text{RP} = 0.97 \times \left(1 – \left(1 – 0.98\right) \times \left(1 – 0.95\right)\right) \times 0.93 = 0.901 ]
Therefore, the overall reliability of the product with subcomponents is 0.901, which is still quite reliable.
Control limits are used to determine whether a product is operating as expected or if there are any issues causing deviations. The upper control limit (UCL) and lower control limit (LCL) help monitor these variations. The formulas for calculating the UCL and LCL are:
[ \text{UCL} = M + (3 \times SD) ] [ \text{LCL} = M – (3 \times SD) ]
Where M is the mean, and SD is the standard deviation. For example, with a mean (M) of 30.006 and a standard deviation (SD) of 0.035, the calculations are:
[ \text{UCL} = 30.006 + (3 \times 0.035) = 30.006 + 0.105 = 30.111 ]
[ \text{LCL} = 30.006 – (3 \times 0.035) = 30.006 – 0.105 = 29.901 ]
Thus, the UCL is 30.111, and the LCL is 29.901, which indicates the acceptable operating range for the product.
Analysis | Formula | Result |
---|---|---|
Break-Even Analysis | BEU = FC / (P – VC) | BEU = 2,000 units |
Contribution to Profit | CP = (P – VC) * UV – FC | CP = $80,000 |
Product Reliability | RP = R1 R2 R3 R4 R5 | RP = 0.979 |
Reliability with Subcomponents | RP = SC1R (1 – (1 – SC2R) (1 – SC3R)) * SC4R | RP = 0.901 |
Control Limits | UCL = M + (3 SD), LCL = M – (3 SD) | UCL = 30.111, LCL = 29.901 |
In order to determine how many units need to be sold to break even, it is essential to conduct a break-even analysis. This analysis helps in establishing the ideal price point for the product, in this case, the pump. The key variables are:
The break-even units (BEU) can be calculated using the formula:
[ \text{BEU} = \frac{\text{FC}}{\text{P} – \text{VC}} ]
Substituting the values:
[ \text{BEU} = \frac{100,000}{100 – 50} = \frac{100,000}{50} = 2,000 ]
This means 2,000 units must be sold to break even.
The selling price of a product plays a crucial role in determining the profit margin. While higher prices generally increase the profit per unit, they can also reduce the number of units sold, potentially impacting overall profits. To determine the most profitable price point, a contribution to profit (CP) analysis is essential. The formula for CP is:
[ \text{CP} = (\text{P} – \text{VC}) \times \text{UV} – \text{FC} ]
Where UV represents the units sold. Two price points are considered:
[ \text{CP} = (100 – 50) \times 3,600 – 100,000 = 50 \times 3,600 – 100,000 = 180,000 – 100,000 = 80,000 ]
[ \text{CP} = (110 – 50) \times 2,900 – 100,000 = 60 \times 2,900 – 100,000 = 174,000 – 100,000 = 74,000 ]
From this analysis, it is clear that the more profitable price point is $100 per pump.
Reliability testing focuses on evaluating the functionality and durability of a product. The goal is to assess how long the product will last, thus minimizing the likelihood of defective or returned items. To determine the overall reliability of a product, the following formula is used:
[ \text{RP} = R1 \times R2 \times R3 \times R4 \times R5 ]
Substituting the reliability values for each component:
[ \text{RP} = 0.997 \times 0.998 \times 0.995 \times 0.999 \times 0.990 = 0.979 ]
Thus, the overall reliability of the product is 0.979, indicating high reliability.
When a company manufactures multiple products with various subcomponents, it is important to evaluate the reliability of the entire system, not just individual components. A product’s overall reliability can be calculated by considering the reliability of its subcomponents. The formula used is:
[ \text{RP} = \text{SC1R} \times \left(1 – \left(1 – \text{SC2R}\right) \times \left(1 – \text{SC3R}\right)\right) \times \text{SC4R} ]
Using the following reliability values for the subcomponents:
[ \text{RP} = 0.97 \times \left(1 – \left(1 – 0.98\right) \times \left(1 – 0.95\right)\right) \times 0.93 = 0.901 ]
Therefore, the overall reliability of the product with subcomponents is 0.901, which is still quite reliable.
Control limits are used to determine whether a product is operating as expected or if there are any issues causing deviations. The upper control limit (UCL) and lower control limit (LCL) help monitor these variations. The formulas for calculating the UCL and LCL are:
[ \text{UCL} = M + (3 \times SD) ] [ \text{LCL} = M – (3 \times SD) ]
Where M is the mean, and SD is the standard deviation. For example, with a mean (M) of 30.006 and a standard deviation (SD) of 0.035, the calculations are:
[ \text{UCL} = 30.006 + (3 \times 0.035) = 30.006 + 0.105 = 30.111 ]
[ \text{LCL} = 30.006 – (3 \times 0.035) = 30.006 – 0.105 = 29.901 ]
Thus, the UCL is 30.111, and the LCL is 29.901, which indicates the acceptable operating range for the product.
Analysis | Formula | Result |
---|---|---|
Break-Even Analysis | BEU = FC / (P – VC) | BEU = 2,000 units |
Contribution to Profit | CP = (P – VC) * UV – FC | CP = $80,000 |
Product Reliability | RP = R1 R2 R3 R4 R5 | RP = 0.979 |
Reliability with Subcomponents | RP = SC1R (1 – (1 – SC2R) (1 – SC3R)) * SC4R | RP = 0.901 |
Control Limits | UCL = M + (3 SD), LCL = M – (3 SD) | UCL = 30.111, LCL = 29.901 |
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