← Back to topic
Vidaara.orgClass 12 · Mathematics
CodeVID-M12-14-MAR-01
Marginal Functions & Elasticity — Assignment
Chapter: Application of Calculus in Commerce
Topic: Marginal Functions & Elasticity of Demand
Maximum Marks: 35
Time: 75 minutes
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.
Marginal revenue is:
  • A.$R(x)/x$
  • B.$\dfrac{dR}{dx}$
  • C.$\int R\,dx$
  • D.$R-C$
2.
Profit is maximised when:
  • A.$\text{MR}=\text{MC}$
  • B.$\text{MR}=0$
  • C.$\text{MC}=0$
  • D.$R=C$
3.
If $C(x)=x^2+4x+10$, $\text{MC}$ at $x=5$ is:
  • A.$10$
  • B.$14$
  • C.$24$
  • D.$9$
4.
Demand is inelastic when:
  • A.$|E_d|>1$
  • B.$|E_d|<1$
  • C.$|E_d|=1$
  • D.$E_d=0$
5.
Marginal cost is:
  • A.$C(x)/x$
  • B.$\dfrac{dC}{dx}$
  • C.$\int C\,dx$
  • D.$xC$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $C(x)=x^2+4x+10$, find the marginal cost at $x=5$.
7.
If $R(x)=20x-x^2$, find the marginal revenue at $x=3$.
8.
If $P(x)=-x^2+40x-100$, find the profit-maximising output.
9.
If the demand is $x=50-2p$, find the elasticity $E_d$ at $p=10$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If $C(x)=0.005x^3-0.02x^2+30x+5000$, find the marginal cost at $x=3$.
11.
If $R(x)=30x-2x^2$, find the marginal revenue and the output where $\text{MR}=0$.
12.
If the demand is $p=40-x$, write the revenue and marginal revenue functions.
13.
If the demand is $x=20-p$, find the elasticity at $p=5$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The demand function is $p=50-2x$. Find the marginal revenue and the output that maximises revenue.
15.
The total cost is $C(x)=x^3-6x^2+15x$. Find the marginal cost and the value of $x$ at which it is minimum.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\dfrac{dR}{dx}$
  2. (A) $\text{MR}=\text{MC}$
  3. (B) $14$
  4. (B) $|E_d|<1$
  5. (B) $\dfrac{dC}{dx}$
Section B — Short Answer (2 marks)
  1. $14$.
  2. $14$.
  3. $x=20$.
  4. $-\tfrac23$ (inelastic).
Section C — Short Answer (3 marks)
  1. $30.015$.
  2. $\text{MR}=30-4x$; $x=7.5$.
  3. $R=40x-x^2$; $\text{MR}=40-2x$.
  4. $-\tfrac13$ (inelastic).
Section D — Long Answer (5 marks)
  1. $\text{MR}=50-4x$; revenue maximum at $x=12.5$ (max revenue $\textsf{Rs }312.50$).
  2. $\text{MC}=3x^2-12x+15$; minimum at $x=2$ (MC $=3$).
Generated by Vidaara.org · Assignment VID-M12-14-MAR-01 · vidaara.org