Q. 14

# A tank with recta

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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