A tank with a 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 the building of tank costs Rs. 70 per square metre for the base and Rs. 45 per square metre for the sides, what is the cost of least expensive tank?
Given:
Volume = 8
Let C be the cost of the tank then,
Now, differentiating both sides with respect to , we get
For maxima & minima
Again, differentiating both sides w.r.t , we get
When , the cost of the tank is minimum
Substituting the value of in equation (i), we get
Hence, the cost of the least expensive tank is Rs. 1000.