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A square tank of capacity 250 cubic metres has to be dugout. The cost of the land is Rs 50 per square metre. The cost of digging increases with the depth and for the whole tank it is Rs 400 x h2 where h metres is the depth of the tank. What should be the dimensions of the tank so that the cost be minimum? |
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Answer» Let side of square tank = x and depth = h Capacity = x2h = 250 Cost function = c = 50x2 + 400h2 c = 50x2 + 400 x 250 x 250 x-4 dc/dx = 0, x = 10 h = 2.5 d2c/dx2 > 0 local maxima Total cost of tank is minimum when side is 10 metre and depth of tank = 2.5 metre |
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