A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. If building of tank cost Rs 70 per square metre for the base and Rs 45 per square matre for sides, what is the cost of least expensive tank?
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