question_answer 97)

A tank with rectangular base and sides, open at the top of two be constructed so that its depth is 2m. and volume is 8m3. If building of tank costs Rs.70 per m2 for the base and Rs.45 per m2 for sides. What is the cost of least expensive tank ? 

Answer:

Let (x × y × 2) be the tank       V = Volume of tank       = 8m3 (given)                   Area of base of tank (A1) = xy       (A2) Area of 4 walls             = 2(l + b) × h             = 2(x + y) × 2             = 4 (x + y)       of building       C = 70A1 + 45 A2 = 70 xy + 45                      × 4 (x + y)                         [Using (1)]                        ?. (2)                                                             (x > 0)       Now              is minimum when x = 2       Minimum cost of building             = 280 + 180 × 4 = 280 + 720       = Rs.1000.