Application of Calculus - ISC Class 12 Mathematics Questions with Answers, Page 4

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A manufacturer’s marginal cost function is $\frac{500}{\sqrt{2x+25}}$. Find the cost involved to increase production from 100 units to 300 units.

If the demand function is given by $x = \frac{600-p}{8}$, where the price is ₹ $p$ per unit and the manufacturer produces $x$ units per week at the total cost of ₹ $(x^2 + 78x + 2500)$, find the value of $x$ for which the profit is maximum.

[3×2]

A bill of ₹ 60,000 payable 10 months after date was discounted for ₹ 57,300 on 30th June, 2007. If the rate of interest was $11\frac{1}{4}\%$ per annum, on what date was the bill drawn?

The demand for a certain product is represented by the equation $p = 500 + 25x - \frac{x^2}{3}$ in rupees where $x$ is the number of units and $p$ is the price per unit. Find:

The price relatives and weights of a set of commodities are given below:

Commodity	A	B	C	D
Price relatives	125	120	127	119
Weights	$x$	$2x$	$y$	$y + 3$

If the sum of the weights is 40 and weighted average of price relatives index number is 122, find the numerical values of $x$ and $y$.

Construct 3 yearly moving averages from the following data and show on a graph against the original data:

Year	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009
Annual sales in lakhs	18	22	20	26	30	22	24	28	32	35

A machine costs ₹ 60,000 and its effective life is estimated to be 25 years. A sinking fund is to be created for replacing the machine at the end of its life time when its scrap value is estimated as ₹ 5,000. The price of the new machine is estimated to be 100% more than the price of the present one. Find the amount that should be set aside at the end of each year, out of the profits, for the sinking fund if it accumulates at an interest of 6% per annum compounded annually.