Tag: revenue functions from marginal revenue functions

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Multiple choice 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
A firm $ABC$ starts producing pens and finds that the production cost of each pen is Rs $10$, and the fixed expenditures of production is Rs. $4500$. If each pen is sold for Rs. $25$, find break-even point.
  1. $x=200$
  2. $x=100$
  3. $x=400$
  4. $x=300$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Manufacturing cost $=10$
Number of pens $=10$
Total manufacturing cost $=10x+4500$
Selling cost $=25x$
Break even value $\Rightarrow $ manufacturing cost $=$ Selling cost 
$\Rightarrow 10x+4500=25x$
$x=300$
Multiple choice 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
A company sells its product at the rate of Rs. $6$ per unit. The variable costs are estimated to run $25\%$ of the total revenue received. If the fixed costs for the product are Rs. $4500$. Find the total cost function.
  1. $4500x$
  2. $4500x+\dfrac{1}{2}x$
  3. $4500x+\dfrac{3}{2}x$
  4. $4500x+\dfrac{5}{2}x$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  Here, price per unit $(p)=Rs.6$ and fix cost is $Rs.4500$.

$\Rightarrow$  $Total\,\, revenue\,\,R(x)=p.x=6x$  where $x$ is number of unit sold.
$\Rightarrow$  $Total\, \,cost\,\, function\,\,C(x)=4500x+\dfrac{25}{100}R(x)$
$\Rightarrow$  $C(x)=4500x+\dfrac{25}{100}\times 6x$

$\Rightarrow$  $C(x)=4500x+\dfrac{3}{2}x$ 

Multiple choice 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
A company sells its product at the rate of Rs. $6$ per unit. The variable costs are estimated to run $25\%$ of the total revenue received. If the fixed costs for the product are Rs. $4500$. Find the profit function.
  1. $6x-\dfrac{3}{2}x-4500$
  2. $6x-\dfrac{1}{2}x-4500$
  3. $6x+\dfrac{3}{2}x-4500$
  4. $6x-\dfrac{5}{2}x+4500$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  Here, price per unit $(p)=Rs.6$

$\Rightarrow$  Total revenue $R(x)=p.x=6x$  where $x$ is the number of unit sold.
$\Rightarrow$  Cost function $C(x)=4500+\dfrac{25}{100}R(x)$

$\Rightarrow$  Cost function $C(x)=4500+\dfrac{25}{100}\times 6x$

$\Rightarrow$   $C(x)=4500+\dfrac{3}{2}x$

$\Rightarrow$   Profit function $P(x)=R(x)-C(x)$

$\Rightarrow$  $P(x)=6x-(4500+\dfrac{3}{2}x)$

$\therefore$    $P(x)=6x-\dfrac{3}{2}x-4500$

Multiple choice 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

Find the elasticity of supply when price $5$ units. Supply function is given by $q = 25 - 4p +p^2$

  1. $1$
  2. $2$
  3. $0$

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$q=25-4p+p^{2}$
Elasticity of supply $=\cfrac{\cfrac{dq}{q}}{\cfrac{dp}{p}}=\cfrac{(-4+2p)\times p}{(25-4p+p^{2})}$
When $p=5$ units
Elasticity of supply $=\cfrac{(-4+10)\times 5}{(25-20+25)}=1$
Multiple choice 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

Find the elasticity of supply for supply function $x = 2p^2+5$, when $p=3$.

  1. $\dfrac{23}{36}$
  2. $\dfrac{36}{23}$
  3. $\dfrac{63}{32}$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Elasticity of supply$\Rightarrow\cfrac{\cfrac{+dx}{x}}{\cfrac{dp}{p}}$$\Rightarrow\cfrac{(4p)p}{2p^{2}+5}$
Elasticity of supply when $p=3\Rightarrow\cfrac{36}{23}$
Multiple choice 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

A village road is to be constructed by a team of $250$ workers. After $12$ days it was found that only $2/7^{th}$ part of the work was complete. To complete the rest in another $25$ days, how many more workers should be employed?

  1. $53$
  2. $52$
  3. $55$
  4. $50$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the total unit of work be $7$ units.
According to question,
$\dfrac {M _{1}D _{1}}{W _{1}} = \dfrac {M _{2}D _{2}}{W _{2}} \Rightarrow \dfrac {250\times 12}{2} = \dfrac {M _{2}\times 25}{(7 - 2)} \Rightarrow M _{2} = 300$
Number of extra workers needed $= 300 - 250 = 50$.

Multiple choice 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

A railway half ticket costs half the full fare but reservation charge is same. One reserved ticket from Ranchi to Howrah cost $Rs.1720$ and one full and one half ticket (both reserved) costs $Rs.2610$. Thus, the reservation charge is

  1. $Rs.60$
  2. $Rs.30$
  3. $Rs.40$

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the full ticket cost $ Rs  \ x $and reservation charge be $ y $
As per given statements,
$ x + y = 1720 $    -(1)
And $ x + y + \frac {x}{2} + y = 2610 => \frac {3x}{2} + 2y = 2610 $ --- (2)

Multiplying equation  $ (1) $ with $ 2 $ we get, $ 2x + 2y
= 3440 $ ----- equation $ (3) $

Subtracting equation $ (2) $

from $ (3) $, we get $ \frac{x}{2} = 830 => x = 1660 $

Substituting $ x = 1660 $ in the equation $ (1) $, we get $ 1660 +y = 1720 => y = 60 $ 

Thus reservation charges were Rs $60 $