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A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. If building of tank costs Rs 70 per sq meters for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?
Asked by Swati Last Modified
Answer Let l, b, and h represent the length, breadth, and height of the tank respectively.
Then, we have height (h) = 2 m
Volume of the tank = 8m3
Volume of the tank = l × b × h
∴ 8 = l × b × 2
Now, area of the base = lb = 4
Area of the 4 walls (A) = 2h (l + b)
However, the length cannot be negative.
Therefore, we have l = 4.
Thus, by second derivative test, the area is the minimum when l = 2.
We have l = b = h = 2.
∴Cost of building the base = Rs 70 × (lb) = Rs 70 (4) = Rs 280
Cost of building the walls = Rs 2h (l + b) × 45 = Rs 90 (2) (2 + 2)
= Rs 8 (90) = Rs 720
Required total cost = Rs (280 + 720) = Rs 1000
Hence, the total cost of the tank will be Rs 1000.
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