# <span lang="EN-US

Let the length and width of base of tank be l and b. Given that the height of tank is 2m and it’s volume is 8 m3.

The volume of a cuboid, of length l, width b and height h, is defined by

V(l,b,h)=lbh

Hence, we get 8=lb× 2 or lb=4m2

or

Let the total cost of building tank be T.

Then T(l,b,h)=70lb+45(lh + bh + lh + bh)

=70lb + 90lh + 90bh

Substituting values of h and lb, we get

T=70×4 +180(l + b)

=280+180(l + b)

Since , we get

Differentiating with respect to b, we get

Differentiating with respect to b, we get

For minima, and

b2=4 or b=2m

At b = 2 m,

T = 280 + 180(2+2)
= 280 + 180(4)
= 280 + 720
= 1000

,

hence b=2m is a point of minima for function T and T(2)=1000 is the least expensive tank.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

If the sum of theMathematics - Board Papers

A metal box with Mathematics - Board Papers

Show that aRD Sharma - Volume 1

Find the local maMathematics - Board Papers

Prove that the seMathematics - Board Papers

Prove that the raMathematics - Board Papers

Prove that the leMathematics - Board Papers