 Hi and welcome to our session. Let us discuss the following question. It says a tank with a rectangular base and rectangular sides open at the top is to be constructed so that its depth is 2 meters and volume is 8 meter cube. A building of a tank costs to be 70 per square meters for the base and rupees 25 per square meter for sides. What is the cost of least expensive tank? Let us now begin with the solution. Now suppose this is the tank which is rectangular sides and rectangular base. Let x and y be the length and width of the tank and we are given in the question that its depth is 2 meters. v is the volume of the tank plus v is equal to 2xy as volume of cuboid is equal to length into width into height. Now here length and width of the tank are x and y and its depth is 2. And in the question we are given that its volume is equal to 8 meter cube. So 2xy is equal to 8. This implies xy is equal to 4 and this implies y is equal to 4 by x. Now total surface area of the tank is equal to xy plus 4x Now y is equal to 4 by x so this is equal to x into 4 by x and this is equal to 4 plus 16 by x plus 4x. Note this area by a. So a is equal to 4 plus 16 by x plus 4x. Let us name this as equation number 1. From differentiating 1 with respect to x we get ta by dx equals to minus 16 by x square plus 4. Now for maximum we will put ta by dx as 0. Now this implies minus 16 by x square plus 4 is equal to 0. This implies 4x square is equal to 16. This implies x square is equal to 4 and this implies x is equal to 2. Now y is equal to 4 by x so this is equal to 4 by 2 and this is equal to 2. This implies length and breadth and is cost of the area of the base at the rate of rupees 70 per square meter. Now this will be equal to into 70 that is 280 rupees. Now cost of area of 4 volts rupees 45 per square meter is equal to 16 into 45 and this is equal to 720 rupees. So total cost is 280 plus 720 rupees that is 1000 rupees. See that e to a by dx2 is equal to minus 16 into minus 2x by x to the power 4 and this is equal to 32 by x cube which is written as 0. So hence we can say that a is minimum breadth and height are equal to 2 meters 1000. This is a required answer. So this completes the session. Bye and take care.