Tag: business mathematics and statistics

Questions Related to business mathematics and statistics

State whether the following statements are 'true' or 'false':
Each unit of the populations is examined in census inquiry.

business mathematics and statistics sampling methods population and sampling basic concepts of sampling sampling techniques and statistical inference

  1. True

  2. False

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Correct Option: A

State whether the following statements are 'true' or 'false':
A sampling method that divides the population into homogeneous groups from which random samples are drawn is known as systematic sampling.

business mathematics and statistics sampling methods population and sampling basic concepts of sampling sampling techniques and statistical inference

  1. True

  2. False

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Correct Option: A

State whether the following statements are 'true' or 'false':
In simple random sampling method, each unit of the population has an equal chance of being included in the sample.

business mathematics and statistics sampling methods population and sampling basic concepts of sampling sampling techniques and statistical inference

  1. True

  2. False

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Correct Option: A

State whether the following statements are 'true' or 'false':
When properties of the units of the population have more dissimilarities, the use of stratified random sampling method is advantageous. 

business mathematics and statistics sampling methods population and sampling basic concepts of sampling sampling techniques and statistical inference

  1. True

  2. False

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Correct Option: A

Population are unlimited in size are referred to as____________.

business mathematics and statistics sampling methods population and sampling basic concepts of sampling sampling techniques and statistical inference

  1. infinite populations.

  2. finite populations.

  3. census method.

  4. none of the above

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Correct Option: A
Explanation:

Population refers to an entire set of people or objects present for the purpose of gathering data and when the population is unlimited in size i.e. it cannot be ascertained easily, it is known as infinite population.

The demand function if $p = 60 + 2D - 10D^2$, the rate of charge in price with respect to demand is ______

business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

  1. $\dfrac{60}{D} + 2 - 10D$

  2. $2 - 20D$

  3. $2 - 40D$

  4. None of these

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Correct Option: B

Given the total cost function, $TC = a+bQ+cQ^2+dQ^3$, Find the Marginal cost.

business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

  1. $b+2cQ+3dQ^2$

  2. $a + b+2cQ+3dQ^2$

  3. $a + 2b+2cQ+3dQ^2$

  4. None

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Correct Option: A
Explanation:

$\Rightarrow$  We have $TC=a+bQ+cQ^2+dQ^3$

$\Rightarrow$  $Marginal\,cost = \dfrac{d}{dQ}TC$

$\Rightarrow$  $Marginal\, cost=\dfrac{d}{dQ}(a+bQ+cQ^2+dQ^3)$

$\therefore$    $Marginal\,cost=b+2cQ+3dQ^2$

 The total cost function is $TC = 12x + 2x^2$. Find the $MC$.

business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

  1. $12-4x$

  2. $4x - 12$

  3. $12 + 4x$

  4. None of these

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Correct Option: C
Explanation:

$MC = \dfrac{\mathrm{d} TC}{\mathrm{d} x}$

$TC = 12x + 2x^{2}$
$\Rightarrow \dfrac{\mathrm{d} TC}{\mathrm{d} x}=12+4x$
$\Rightarrow MC = 12 + 4x$

$y = 48x - 2x^2$
where, $y=$ Total revenue $ $ $.
$x = $ Output
At what output is total revenue a maximum?

business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

  1. $2$

  2. $12$

  3. $48$

  4. $4$

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Correct Option: B
Explanation:

$\Rightarrow$  We have given, $y=48x-2x^2$

$\Rightarrow$  Differentiate on both sides w.r.t $x$ we get,
$\Rightarrow$  $\dfrac{dy}{dx}=48-4x$          --- ( 1 )
$\Rightarrow$  Let $\dfrac{dy}{dx}=0$
$\Rightarrow$  $48-4x=0$
$\Rightarrow$  $4x=48$
$\Rightarrow$  $x=12$ is a turning point.
$\Rightarrow$  $\dfrac{d^2y}{dx^2}=-4$         [Differentiate ( 1 ) on both sides]
$\Rightarrow$  So, the turning point is a maximum 

The cost, in dollars, of producing $x$ gallons of detergent is given by
$C(x)=350+20x0.08x^2 + 0.0004x^3$
What is a formula for the marginal cost function $C'(x)$

business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

  1. $C(x)=200.16x^2+0.0012x^2$

  2. $C(x)=200.16x+0.0012x^2$

  3. $C(x)=20x0.16x+0.0012x^2$

  4. $C(x)=20x0.16x^2+0.0012x^2$

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Correct Option: B
Explanation:
$c'(x)=\cfrac{d}{dx}(c(x))$
$=2\times(100+0.8)x+3\times0.0004x^{2}$
$=200.16x+0.0012x^{2}$