Vidaara.orgClass 12 · Mathematics
CodeVID-M12-14-CRP-01
Cost, Revenue & Profit Functions — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
Profit function is:
- A.$R(x)+C(x)$
- B.$R(x)-C(x)$
- C.$C(x)-R(x)$
- D.$R(x)\cdot C(x)$
2.
Break-even occurs when:
- A.$R=2C$
- B.$P(x)=0$
- C.$C=0$
- D.$R=0$
3.
If $C(x)=2x+50$ and $R(x)=7x$, the break-even output is:
- A.$5$
- B.$10$
- C.$50$
- D.$7$
4.
Average cost is:
- A.$C(x)\cdot x$
- B.$\dfrac{C(x)}{x}$
- C.$C'(x)$
- D.$R-C$
5.
Revenue $R(x)$ equals:
- A.$C(x)+P(x)$
- B.$p\cdot x$
- C.$\dfrac{C}{x}$
- D.$C-P$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
If $C(x)=2x+50$ and the price is $\textsf{Rs }7$ per unit, write the profit function.
7.
Find the break-even output for $C(x)=2x+50,\ R(x)=7x$.
8.
If $C(x)=x^2+10x+100$, find the average cost at $x=10$.
9.
If the demand is $p=20-x$, write the revenue function.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
If $C(x)=3x+40$ and price is $\textsf{Rs }8$, find the profit function and break-even output.
11.
If $R(x)=50x-x^2$, find $R$ at $x=10$.
12.
Find the average cost of $C(x)=2x^2+5x+18$ at $x=3$.
13.
If the demand is $p=100-2x$, write the revenue function and find $R$ at $x=10$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
The cost is $C(x)=x^2+2x+10$ and the selling price is $\textsf{Rs }22$ per unit. Find the profit function and the output for maximum profit.
15.
A firm has fixed cost $\textsf{Rs }2000$ and variable cost $\textsf{Rs }10$ per unit; each unit sells for $\textsf{Rs }50$. Find the profit function and break-even quantity.
Answer Key
Section A — Multiple Choice Questions
- (B) $R(x)-C(x)$
- (B) $P(x)=0$
- (B) $10$
- (B) $\dfrac{C(x)}{x}$
- (B) $p\cdot x$
Section B — Short Answer (2 marks)
- $P(x)=5x-50$.
- $x=10$.
- $30$.
- $R(x)=20x-x^2$.
Section C — Short Answer (3 marks)
- $P(x)=5x-40$; break-even at $x=8$.
- $400$.
- $17$.
- $R(x)=100x-2x^2$; $R(10)=800$.
Section D — Long Answer (5 marks)
- $P(x)=-x^2+20x-10$; maximum at $x=10$ (profit $\textsf{Rs }90$).
- $P(x)=40x-2000$; break-even at $x=50$ units.
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