Math Problem Statement

Find the missing quantities in the table given the cost of $19.84, breakeven point of $27.84, reduced price of $17.46, and missing operating and absolute losses. Options provided for operating expenses, operating loss, and absolute loss.

Solution

To solve the problem presented in the image, we need to calculate the missing values based on the data provided.

Step-by-step breakdown:

Given Values:

  1. Cost: $19.84
  2. Breakeven Point: $27.84
  3. Reduced Price: $17.46
  4. Operating Expense: ?
  5. Operating Loss: ?
  6. Absolute Loss: ?

Approach:

  1. Operating Expense: The operating expense can be calculated using the breakeven point formula: Breakeven Point=Cost+Operating Expense\text{Breakeven Point} = \text{Cost} + \text{Operating Expense} So, Operating Expense=Breakeven PointCost\text{Operating Expense} = \text{Breakeven Point} - \text{Cost} Operating Expense=27.8419.84=8.00\text{Operating Expense} = 27.84 - 19.84 = 8.00

  2. Operating Loss: The operating loss occurs when the reduced price is less than the breakeven point. The formula is: Operating Loss=Reduced PriceCost\text{Operating Loss} = \text{Reduced Price} - \text{Cost} Operating Loss=17.4619.84=2.38\text{Operating Loss} = 17.46 - 19.84 = -2.38 Since the result is negative, this is a loss of $2.38.

  3. Absolute Loss: The absolute loss includes both the operating expense and the operating loss. It's calculated as: Absolute Loss=Operating Loss+Operating Expense\text{Absolute Loss} = \text{Operating Loss} + \text{Operating Expense} Absolute Loss=2.38+8.00=5.62\text{Absolute Loss} = -2.38 + 8.00 = 5.62

    Note: There seems to be some confusion with the values provided in the options. I'll now check the options to see which one fits these calculations.

Checking Options:

  • A: Incorrect.
  • B: Operating expense is $8.00, which matches, and the operating loss of $2.38 is also correct. However, the absolute loss is not $2.38.
  • C: Incorrect because the operating expense is $10.38.
  • D: Incorrect due to mismatch in absolute loss.

Thus, option B fits most of the calculated values.

Would you like more details or have any questions on this solution?

Here are some relative questions you can explore:

  1. What is the significance of breakeven points in business analysis?
  2. How is operating loss different from absolute loss?
  3. Can operating expenses fluctuate based on external factors?
  4. What strategies can businesses use to minimize absolute losses?
  5. How can companies adjust prices to avoid operating losses?

Tip: When calculating losses, always distinguish between fixed costs (like operating expenses) and variable costs (like production costs), as they affect different parts of profit analysis.

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Math Problem Analysis

Mathematical Concepts

Cost Analysis
Breakeven Point
Profit and Loss

Formulas

Breakeven Point = Cost + Operating Expense
Operating Loss = Reduced Price - Cost
Absolute Loss = Operating Loss + Operating Expense

Theorems

Basic Profit and Loss Calculation

Suitable Grade Level

Grades 10-12