Question

Solution

Correct option is Let 2x be the length, x be the width and y be the height of the box.

Volume = C = 2x2 y.

Let then cost of bottom = Rs. k per sqm.

Total cost = cost of bottom + cost of other faces  Eliminating y using C = 2x2y,

Total cost = 2k(4x2 + 9C/2x

Total cost is to be minimized       The dimensions are: SIMILAR QUESTIONS

Q1

Find points of local maximum and local minimum of Q2

Find the point of local maximum and local minimum of Q3

Find points of local maximum and local minimum of f(x) = x2 ex.

Q4

Find points of local maximum and local minimum of (x) = x2/3 (2x – 1).

Q5

Identify the absolute extrema for the following function.

f (x) = x2 on [–1, 2]

Q6

Identify the absolute extrema for the following function.

f (x) = x3   or    [–2, 2]

Q7

Determine the absolute extrema for the following function and interval.

g(t) = 2t3 + 3t2 – 12t + 4    on    [– 4, 2]

Q8

Find the local maximum and local minimum values of the function y = xx.

Q9

A window is in the form of a rectangle surmounted by a semi-circle. The total area of window is fixed. What should be the ratio of the areas of the semi-circular part and the rectangular part so that the total perimeter is minimum?

Q10

Find the maximum surface area of a cylinder that can be inscribed in a given sphere of radius R