2. An expression for a company's cost to make n bicycles is -0.017n? - 6.8n + 690. An expression for the revenue from selling these n bicycles is 70n. Profit is revenue minus cost. Which is an expression for the profit for making and selling n bicycles?
Answer: D
-0.017n^2 + 63.2n + 690
The expression for the profit from making and selling n bicycles is given by subtracting the cost from the revenue. By calculating the profit using the provided cost and revenue functions, we derive the expression as -0.017n^2 + 63.2n + 690.
A) -0.017n^2 - 76.8n + 690
This option incorrectly combines the revenue and cost functions. The negative coefficient for n in this expression suggests a misunderstanding of how to calculate profit, which should result in a positive linear term when revenue exceeds costs.
B) 0.017n^2 + 76.8n - 690
This option is incorrect because it presents a positive quadratic term and a linear term that does not align with the profit calculation. The profit must reflect the subtraction of costs from revenue, leading to a negative quadratic term instead.
C) 0.017n^2 + 63.2n + 690
While this option has a correct linear term, it fails due to the positive quadratic coefficient. The profit function derived from the revenue minus cost should result in a negative quadratic term, indicating diminishing returns as production increases.
D) -0.017n^2 + 63.2n + 690
This is the correct expression for the profit, as it accurately reflects the revenue minus the cost. The negative coefficient of n^2 indicates decreasing profitability with increased production, while the linear term accurately represents the revenue exceeding fixed costs.
Conclusion
The correct answer, -0.017n^2 + 63.2n + 690, effectively captures the relationship between production costs and revenue, demonstrating that profit is maximized at specific production levels. All other options misrepresent this relationship through incorrect coefficients or terms, failing to adhere to the fundamental profit calculation principles.