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 cm^{3}

lbh = 8

2lb = 8 (given)

lb = 4

b = …1

Cost for building base = Rs 70/m^{2}

Cost for building sides = Rs 45/m^{2}

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

l^{2} = 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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