InterviewSolution
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InterviewSolution
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with its vertex at one end of the major axis.9. A tank with rectangular base and rectangular sides, open at the top is to beconstructed so that its depth is 2 m and volume is 8 m. If building of tank costsRs 70 per sq metres for the base and Rs 45the cost of least expensive tank?per square metre for sides. What is |
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Answer» Step 1:Let the length and breadth of the tank be x metre and y metro respectively. The depth of it is 2m.Volume of tank = 2×x×y = 2xyVolume = 8m3⇒ 2xy = 8 xy = 4-----(1) Step 2:Area of base = xyArea of sides = 2.2(x+y) = 4(x+y)Cost of construction= Rs[70xy+45×4(x+y)] = Rs[70xy+180(x+y)] = Rs[70xy+180(x+y)]-----(2) Step 3:Put the value of y in (2) from (1) we havexy = 4y = 4/xC = 70.4 + 180(x + (4/x)) = 280 + 180(x + (4/x)) Step 4:Differentiating with respect to x we get,dc/dx = 0 + 180(1 − 4x^2) = 180((x^2−4)/x^2) Step 5:For maxima or minima dc/dx=0x^2 − 4=0x2 = 4x = ±2dc/dx changes sign from -ve to +ve at x=2∴c is maximum at x=2[length of the tank cannot be negative]⇒x=2 and y = 4/xy = 4/2 = 2Thus tank is a cube of side 2m Step 6:Least cost of construction = Rs[280 + 180(2 + 4/2)] = Rs [280 + 720] = Rs1000 |
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