Question

A box of constant volume C is to be twice as long as it is wide. The cost per unit area of the material on the top and four sides is three times the cost for bottom. What are the most economical dimensions of the box?  

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

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Find points of local maximum and local minimum of 

Q2

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

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Q5

Identify the absolute extrema for the following function.  

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Q6

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Q7

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             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