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Home » A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m^3 . If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?
A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m^3 . If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?
Applications of Derivatives | CBSE | Class 12 | Maths | Miscellaneous | NCERT
A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m^3 . If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?

Given: Depth of tank = 2 m

Let  m be the length and  m be the breadth of the base of the tank.

Volume of tank = 8 cubic meters

 

 

 

Cost of building the base of the tank at the rate of ` 70 per sq. meter is 

And cost of building the four walls of the tank at the rate of ` 45 per sq. meter is

= `

Let  be the total cost of building the tank.

 and 

Now 

 

 

 

  [length cannot be negative]

At  [Positive]

 is minimum at .

Minimum cost = 

= 280 + 360 + 360 = ` 1000

i

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