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The quantity of gasoline that is consumed while driving a motor boat varies as the cube of its velocity. Find the most economical speed when going upstream in a river whose speed is 5 miles per hour?
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A 15 ft long cable is to be divided into two parts. One part is to be bent into a circle and the other part is to be bent into a square. How should the 15 ft long cable be divided such that the sum of the areas of the circle and the square is the minimum?
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The total area of a page is 140 square inches. The combined width of the top and bottom margins is 3 inches. The combined width of the left and right margins is 2 inches. What must be the dimensions of the page in order that the area of the page net of the margins (i.e. the printable area) is the maximum?
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Divide 20 into two parts such that the product of one of the parts with the cube of the other part is the maximum?
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The cost of fuel for running a train is proportional to the square of its speed.
The cost of fuel is $ 48 per hour when the train runs at 16 mph. What is the most economical speed of the train if the fixed costs i.e. salaries etc amount to $ 300 per hour?
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A square tank of capacity 300 cubic feet has to be dug out. The cost of land is
$10 per sq.ft. The cost of digging increases with the depth. The cost of digging the tank is $ 400 (h) ², where ‘h’ is the depth to which digging is done. What should be the dimensions of the tank for the least total cost?
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