The monthly net profit, in dollars, for selling handmade candles is given by \(\mathrm{p(q) = 325q - 2,100}\), where q...

1. TRANSLATE the problem information

• Given information:
  • Profit function: \(\mathrm{p(q) = 325q - 2{,}100}\)
  • Number of candles sold: \(\mathrm{q = 36}\)
• What this tells us: We need to find \(\mathrm{p(36)}\)

2. SIMPLIFY by substituting the value

• Replace q with 36 in the function:
  \(\mathrm{p(36) = 325(36) - 2{,}100}\)

3. SIMPLIFY the multiplication first

• Calculate \(\mathrm{325 \times 36}\) using distribution:
  \(\mathrm{325 \times 36 = 325 \times (30 + 6)}\)
  \(\mathrm{= 325 \times 30 + 325 \times 6}\)
  \(\mathrm{= 9{,}750 + 1{,}950}\)
  \(\mathrm{= 11{,}700}\)

4. SIMPLIFY by completing the subtraction

• \(\mathrm{p(36) = 11{,}700 - 2{,}100 = 9{,}600}\)

Answer: B. $9,600

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly set up \(\mathrm{p(36) = 325(36) - 2{,}100}\) but stop after calculating the multiplication, forgetting to subtract 2,100.

They calculate \(\mathrm{325 \times 36 = 11{,}700}\) and think they're done, missing the crucial final step of subtracting the fixed cost.

This leads them to select Choice C ($11,700).

Second Most Common Error:

Order of operations confusion: Students misinterpret the function and add instead of subtract the 2,100.

They calculate: \(\mathrm{325 \times 36 + 2{,}100 = 11{,}700 + 2{,}100 = 13{,}800}\), treating the constant as additional profit rather than a cost to subtract.

This leads them to select Choice D ($13,800).

The Bottom Line:

This problem tests whether students can systematically work through function evaluation without rushing. The key is following through completely: substitute, multiply carefully, then subtract to account for the business costs represented by the -2,100 term.