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Please Solve RD Sharma Class 12 Chapter 17 Maxima and Minima Exercise Case Study Based Questions question 5 subquestion (iii) Maths Textbook Solution.

Answers (1)

Answer: $3600\left(1-\frac{4}{x^{2}}\right)$

Hint: volume $= l\times b\times h$

Solution:

Let c be the total cost of the tank

C(x) = Cost of base + Cost of sides

$=1800 \mathrm{xy}+3600(\mathrm{x}+\mathrm{y}) \rightarrow(1)$

As w know,

Length if the tank $= x$

Breadth of the tank $= y$

Depth of the tank $=\mathrm{h} \\$

$=2 \mathrm{~m} \\$

Volume of the tank $\begin{aligned} & &=8 \mathrm{~m}^{3} \end{aligned}$

$\begin{aligned} &1=x \\ &b=y \\ &h=2 \\ &v=8 m^{2} \end{aligned}$

Volume $=l\times b\times h$

$\begin{aligned} &8=2 \times x \times y \\ &y=\frac{4}{x} \Rightarrow(2) \end{aligned}$

Sub y value in (1)

$\begin{aligned} \mathrm{C}(\mathrm{x}) &=1800 \times\left(\frac{4}{\mathrm{x}}\right)+3600(\mathrm{x}+4) \\ & \end{aligned}$

$\Rightarrow 7200+3600\left(\mathrm{x}+4 \mathrm{x}^{-1}\right) \\$

$\mathrm{c}^{\prime}(\mathrm{x}) =0+3600\left(1+(-1) 4 \mathrm{x}^{-1-1}\right) \\$

$=3600\left(1-4 \mathrm{x}^{-2}\right) \\$

$=3600\left(1-\frac{4}{\mathrm{x}^{2}}\right)$

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