A tank with a rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 4 meter and volume is 36 cubic meters. If building of the tank costs ₹ 100 per square meter for the base and ₹ 50 per square meter for the sides, then the cost of least expensive tank is

Step-by-step solution

Let length and breadth of the tank be ' x ' m and ' y ' m respectively. Height of the tank is 4 ~m . Volume =36 ~m ^3 array ll & 4 x y=36 & x y=9 & y= 9 x array Total area of the tank including sides and base =x y+2(4 x)+2(4 y) ....[From (i) and (ii)] f (x)=9+8 x+8 ( 9 x ) =9+8 x+ 72 x f ^ (x)=8- 72 x^2 f ^ (x)=0 x=3 y=3 Required cost =100 (3 3)+50 aligned & (2 4 3+2 4 3) = & 900+2400 = & ₹ 3300 aligned