Question

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 metre for sides, what is the cost of least expensive tank?

Answer 1

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

Also, assume the volume of tank as V

h = 2 m (given)

V = 8 cm³

lbh = 8

2lb = 8 (given)

lb = 4

b = 4/l …1

Cost for the building base = Rs 70/m²

Cost for the building sides = Rs 45/m²

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

C = lb × 70 + 2(l + b)h × 45

Condition for the maxima and minima

So, cost will be minimum for l = 2

From the equation (1)

C = Rs 1000