Answer :

Let the length, breath and height of tank be l, b and h respectively.


Also, assume volume of tank as V


h = 2 m (given)


V = 8 cm3


lbh = 8


2lb = 8 (given)


lb = 4


b = …1


Cost for building base = Rs 70/m2


Cost for building sides = Rs 45/m2


Cost for building the tank, C = Cost for base + cost for sides


C = lb × 70 + 2(l + b) h × 45


C = l × × 70 + 2(l+) × 2 × 45


C = 280 + 180(l+) …2


Condition for maxima and minima



180(1 - ) = 0



l2 = 4


l = ±2 cm


Since, l cannot be negative


So, l = 2 cm



For l = 2


Therefore, cost will be minimum for l =2


From equation 2


C = 280 + 180(l+)


C = Rs 1000


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