5 Mark Each

Question 15 Marks

The demand function of a commodity is $x=75-\frac
{3 p}{5}$ and the total cost of producing $x$ units is
$\frac{x^2}{5}+13 x+1000$. Obtain the maximum profit.

Answer

The price of mobile phone should be kept $₹ 10,000$ for
maximum profit.
Maximum profit $=680$ at $x=30$

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Question 25 Marks

The total cost of manufacturing $x$ mobile phones for a
mobile making company is $\frac{x^2}{20}+4 x+30$.
If the demand function of mobile phone is
$(p=\frac{30-x}{2})$, where $p=$ price(in thousand rupees), how many mobile phones should be produced to earn maximum profit? What price should be fixed for the maximum profit ?

Answer

Maximum profit at $x=10$

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Question 35 Marks

During summer, a local potter makes one refrigerator in 5
thousand rupees using clay and other materials. The
demand function of such a refrigerator is $p=21-x$,
where $p=$ price (in thousand rupees) and $x=$
demand of refrigerator. How many refrigerators should
the potter make to get maximum profit? Also obtain
the maximum profit.

Answer

Maximum profit $=64$ at $x=8$

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Question 45 Marks

Obtain the maximum and minimum values of a function
$f(x)=4 x+\frac{1}{x}-3$.

Answer

Maximum value $=-7$, Minimum value $-1$

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Question 55 Marks

Obtain the maximum and minimum values of a function
$y=x^3-3 x^2-45 x+12$.

Answer

Maximum value $=93$, Minimum value $=-163$