The total cost, in dollars, for a company to produce n units of a certain product can be modeled by...
GMAT Advanced Math : (Adv_Math) Questions
The total cost, in dollars, for a company to produce \(\mathrm{n}\) units of a certain product can be modeled by the function \(\mathrm{C(n) = 1,200 + 4.5n}\). Based on the model, which of the following statements is the best interpretation of the equation \(\mathrm{C(300) = 2,550}\)?
1. TRANSLATE the function notation
- Given information:
- \(\mathrm{C(n) = 1,200 + 4.5n}\) represents total cost for n units
- We need to interpret: \(\mathrm{C(300) = 2,550}\)
- What this tells us: We have function notation where something goes in and something comes out
2. TRANSLATE using the standard function pattern
- Function notation always follows: \(\mathrm{f(input) = output}\)
- In our equation \(\mathrm{C(300) = 2,550}\):
- The number 300 is inside the parentheses → this is the input
- The number 2,550 is on the right side of equals → this is the output
3. INFER what each value represents in context
- Input = 300: Since n represents number of units, this means 300 units
- Output = 2,550: Since C(n) represents total cost, this means $2,550 total cost
4. TRANSLATE back to plain English
- Combining our interpretations: "The total cost to produce 300 units is $2,550"
- This matches choice A exactly
Answer: A
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students mix up which number is the input and which is the output in function notation.
They see \(\mathrm{C(300) = 2,550}\) and incorrectly think: "300 is the cost and 2,550 is the number of units." This backwards interpretation comes from not systematically applying the \(\mathrm{f(input) = output}\) pattern.
This may lead them to select Choice B (The cost to produce 2,550 units of the product is $300).
Second Most Common Error:
Poor INFER reasoning: Students correctly identify 300 as units and 2,550 as cost, but misunderstand what type of cost C(n) represents.
They think \(\mathrm{C(300) = 2,550}\) means the cost per unit is $2,550, rather than recognizing that C(n) gives the total cost for n units. The function name "total cost" in the problem statement is the key clue they miss.
This may lead them to select Choice C (When the company produces 300 units, the average cost per unit is $2,550).
The Bottom Line:
This problem tests pure function notation interpretation - success depends entirely on systematically applying the input-output pattern and carefully reading what the function represents.