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


V(l,b,h)=lbh


Hence, we get 8=lb× 2 or lb=4m2


or


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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