Tag: business mathematics and statistics

Questions Related to business mathematics and statistics

Given the marginal cost function $\dfrac{2x}{3}+3-\dfrac{16}{x^2}$, find  average cost function.

business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

  1. $\dfrac{1}{3}x^2+3x-7+\dfrac{16}{x}$

  2. $\dfrac{1}{2}x^2+3x-7+\dfrac{16}{x}$

  3. $\dfrac{1}{4}x^2+3x-7+\dfrac{16}{x}$

  4. None of these

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  We have $MC=\dfrac{2x}{3}+3-\dfrac{16}{x^2}$


$\Rightarrow$  $Average\,\,cost=\int (MC)dx$ 


$\Rightarrow$   $Average\,\,cost=\int (\dfrac{2x}{3}+3-\dfrac{16}{x^2})dx$


$\therefore$   $Average\,\,cost=\dfrac{2x^2}{2\times 3}+3x-7+\dfrac{16}{x}$

$\Rightarrow$   $Average\,\,cost=\dfrac{1}{3}x^2+3x-7+\dfrac{16}{x}$

The cost function of a firm $C(x)=3x^2-2x+3$. Find the average cost when $x=3$.

business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

  1. 8

  2. 9

  3. 10

  4. 12

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  We have, $C(x)=3x^2-2x+3$

$\Rightarrow$  Average cost = $\dfrac{C(x)}{x}$

$\Rightarrow$  Average cost = $\dfrac{3x^2-2x+3}{x}$

$\Rightarrow$  Average cost = $3x-2+\dfrac{3}{x}$.

$\Rightarrow$  Substitute value of $x=3$,
$\Rightarrow$  Average cost = $3\times 3-2+\dfrac{3}{3}=9-2+1=8$
$\therefore$    $Average\, cost\,=8$. 

If the demanding Law is given by $q = \dfrac{20}{p+1}$, find the elasticity of demand with respect to price at the point when $p = 3.$

business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

  1. $\dfrac43$

  2. $-\dfrac34$

  3. $\dfrac23$

  4. $-\dfrac32$

Show answer
Correct Option: B
Explanation:
Elasticity of demand $=\cfrac{\cfrac{dq}{q}}{\cfrac{dp}{p}}=-\cfrac{p}{(p+1)}$
When $p=3$
Elasticity of demand $=-\cfrac{3}{4}$

If the total cost function for a manufacturer is given by $C =\dfrac{5x^2}{\sqrt(x^2+3)}+5000$, find marginal cost function.

business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

  1. $\dfrac{3x(x^2+6)}{(x^2+3)^{(3/2)}}$

  2. $\dfrac{4x(x^2+6)}{(x^2+3)^{(3/2)}}$

  3. $\dfrac{5x(x^2+6)}{(x^2+3)^{(3/2)}}$

  4. None of these

Show answer
Correct Option: C
Explanation:

Given cost function $C\left(x\right)=\dfrac{5x^2}{\sqrt{\left(x^2+3\right)}}+5000$


Marginal cost function is given by $C'\left(x\right)$

$C'\left(x\right)=\dfrac{\left(\sqrt{x^2+3}\right)\left(10x\right)-\dfrac{5x^2}{2\sqrt{x^2+3}}\times\left({2x+10}\right)}{\left(\sqrt{x^2+3}\right)^2}$

$\dfrac{d}{dx}\left(\dfrac{u}{v}\right)=\dfrac{v\dfrac{du}{dx}-u\dfrac{dv}{dx}}{v^2}$

$C'\left(x\right)=\dfrac{2\left(x^2+3\right)\left(10x\right)-5x^2\left(2x\right)}{2\left(\sqrt{x^2+3}\right)^3}=\dfrac{5x\left(x^2+6\right)}{\left(x^2+3\right)^\tfrac{3}{2}}$

State, which of the following variables are continuous and which are discrete :


Sizes of shoes is discrete
If true then enter $1$ and if false then enter $0$

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. $1$

  2. $0$

  3. Can't determine

  4. None of these

Show answer
Correct Option: A
Explanation:

Size of a shoe can have integer values only. Hence, it is a discrete variable.

Say true or false:
Daily temperature is discrete variable.

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

Daily temperature can have any integer as well as rational values. Hence, it is a continuous variable.

Say true or false:

Sizes of the shoe are discrete variables.

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Size of shoe can have have only integer value. Hence, it is a discrete variable.

Are you a girl or boy is an example of ______ variable.

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. continuous

  2. dependent

  3. discrete

  4. nominal

Show answer
Correct Option: C
Explanation:

A discrete variable is a variable whose value is obtained by counting.
So, are you a girl or boy is an example of discrete variable.
Since it is answerable.

Which one of the statement is discrete variable?

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. weight of animals in zoo

  2. distance travelled between colleges

  3. number of heads by flipping a coins

  4. height of animals in park

Show answer
Correct Option: C
Explanation:

Discrete variables are countable in a finite amount of time.
So, number of heads when flipping a coin is a discrete variable statement because once the coin is flipped, we will get head or tail result.

The statement "number of heads when flipping a coin" is an example of ______ variable.

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. continuous

  2. dependent

  3. discrete

  4. nominal

Show answer
Correct Option: C
Explanation:

Discrete variables are countable in a finite amount of time.
So, number of heads when flipping a coin is a discrete variable statement because once the coin is flipped, we will get head or tail result.