BusyBee Cleaning Co. is evaluating its costs to clean a standard office. Here is their estimated cost structure:

y = $25x+ $75

y = total cost to clean an office

x = hours spent cleaning an office

What is the best description of the costs of cleaning an office based on this regression analysis?*Source: Retired ICMA CMA Exam Questions.

Question

BusyBee Cleaning Co. is evaluating its costs to clean a standard office. Here is their estimated cost structure:

y = $25x+ $75

y = total cost to clean an office

x = hours spent cleaning an office

What is the best description of the costs of cleaning an office based on this regression analysis?*Source: Retired ICMA CMA Exam Questions.

BlackTom AI · Accepted Answer

The equation y = 25x + 75 identifies a slope of 25 and an intercept of 75, so the slope represents variable cost per hour and the intercept represents fixed cost.

1. Relevant knowledge points and concepts
- In a linear cost function y = mx + b, m (slope) is the variable cost per unit of activity (here per hour) and b (intercept) is the fixed cost incurred even when activity is zero. 
- Variable costs change with x; fixed costs do not.

2. Step-by-step reasoning
- Compare y = 25x + 75 to the general form y = mx + b. Here m = 25 and b = 75.
- Interpret m: 25 is the change in total cost y for each additional hour x → $25 per hour variable cost.
- Interpret b: when x = 0, y = 75 → $75 incurred even with zero hours → fixed cost.

3. Calculations and intermediate steps
- If x = 0: y = 25(0) + 75 = 75 → fixed cost = $75.
- If x = 1: y = 25(1) + 75 = 100.
- Change from x = 0 to x = 1: 100 − 75 = 25 → variable cost per hour = $25.
- For x = 3: y = 25(3) + 75 = 75 + 75 = 150; average cost per hour = 150/3 = $50 (illustrates average depends on hours).

4. Why the correct answer is correct
- The slope (25) directly measures cost added per additional hour (variable). The intercept (75) is cost present with zero hours (fixed). Thus the best description: $25 variable cost per hour and $75 fixed cost.

5. Why the other choices are incorrect
- Choice 1 (there is $25 of fixed costs and $75 of variable costs per hour): reverses slope/intercept roles, incorrect.
- Choice 2 (cost is $25 per hour): ignores the $75 fixed cost; incomplete.
- Choice 4 (cost is $100 per hour): no basis — slope is 25, not 100.

6. Conclusion
Therefore, the correct description is: There is $25 of variable costs per hour and $75 of fixed costs to clean an office, which matches the provided answer.

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