Q. 243.7( 11 Votes )

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Answer :

Let the length and width of base of tank be l and b. Given that the height of tank is 2m and it’s volume is 8 m3.

The volume of a cuboid, of length l, width b and height h, is defined by


Hence, we get 8=lb× 2 or lb=4m2


Let the total cost of building tank be T.

Then T(l,b,h)=70lb+45(lh + bh + lh + bh)

=70lb + 90lh + 90bh

Substituting values of h and lb, we get

T=70×4 +180(l + b)

=280+180(l + b)

Since , we get

Differentiating with respect to b, we get

Differentiating with respect to b, we get

For minima, and

b2=4 or b=2m

At b = 2 m,

T = 280 + 180(2+2)
= 280 + 180(4)
= 280 + 720
= 1000


hence b=2m is a point of minima for function T and T(2)=1000 is the least expensive tank.

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