Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202619 April 2026Morning ShiftMathematicsApplication of DerivativesActual

A tank with a rectangular base and rectangular sides, open at the top is made. Depth of the tank is 4 m and its volume is 36 cubic meters. For making a tank cost of base material used is Rs. 100 per sq. meter and that of sides is Rs. 50 per sq. meter. Then minimum cost of tank is ..............

Options

  1. ARs. 1100
  2. BRs. 2200
  3. CRs. 3300
  4. DRs. 4400

Correct answer

C. Rs. 3300

Step-by-step solution

Let the length and breadth of the base of the tank be x and y respectively. Given depth h = 4 m and volume V = 36 m ^3 . V = x y h 4xy = 36 xy = 9 Cost of the base = 100 xy = 100 9 = 900 Area of the four sides = 2(xh + yh) = 2(4)(x + y) = 8(x + y) Cost of the sides = 50 8(x + y) = 400(x + y) Total cost C = 900 + 400(x + y) To minimize C , we need to minimize x + y . Using AM-GM inequality for x, y > 0 : x + y 2 xy x + y 2 9 = 6 Minimum value of x + y is 6 , which occurs when x = y = 3 . Minimum cost C = 900 + 400(6

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Consider the quadratic equation a x^2+b x+c=0 , where 2 a+3 b+6 c=0 and let g(x)= a x^3 3 + b x^2 2 +c x . Statement-I : The given quadratic equation ax ^2+ bx + c =0 has at least 2025The difference between the absolute maximum and absolute minimum values of the function f(x)=2 x^3-15 x^2+36 x-30 on [-1,4] is 2025If f(x)=x e^ x(1-x) , x R , then f(x) is 2025The angle between the curves y ^2= x and x ^2= y at the point (1,1) is 2025If the tangent of the curve 4 y^3=3 a x^2+x^3 drawn at the point (a, a) forms a triangle of area 25 24 sq.units with the coordinate axes then a = 2025If the function f(x)= x- ^2 x is defined on the interval [- , ] , then f is strictly increasing in the interval 2025If the Lagrange's mean value theorem is applied to the function f(x)=e^x defined on the interval [1,2] and the value of c (1,2) is k , then e^ k-1 = 2025If the tangent to the curve x y+a x+b y=0 at (1,1) makes an angle Tan ⁻¹ 2 with X -axis, then ab a + b = 2025 Full Application of Derivatives list All MHT CET PYQs