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Q.

A closed rectangular box with a square base is to be made so as to contain 1000 cubic feet. The cost of the material per square foot for the bottom is 15 paisa, for the top 25 paisa, for the sides 20 paisa and the labour charges for making the box are Rs 3. If ‘h’ be the height of the box and ‘x’ be the side of the square base and the cost of the box is minimum then x2+h=

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answer is 110.

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Detailed Solution

cos t  of the box is 
Question Image 
 =40x2+80xh+300
 (x2h=1000h=1000x2)
  C=40x2+80000x+300
 dCdx=080x80000x=0x3=1000x=10
 Question Image
   C is minimum when x = 0
 h=10 

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