# A tank with a rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. If the building of tank costs Rs. 70 per square metre for the base and Rs. 45 per square metre for the sides, what is the cost of least expensive tank?

Given

Volume = 8

Let C be the cost of the tank then,

Now, differentiating both sides with respect to , we get

For maxima & minima

Again, differentiating both sides w.r.t , we get

When , the cost of the tank is minimum

Substituting the value of  in equation (i), we get

Hence, the cost of the least expensive tank is Rs. 1000.

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