Hello can you answer all of these, please? 1) Show that a rectangle with a given area has a minimum perimeter when it is a square. 2) A box with a square base and open top must have a volume of 400 cm^3. Find the dimensions of the box that minimizes the amount of material used. 3) A box with an open top is to be constructed from a square piece of cardboard that is 3 m wide, by cutting out a square from each from each of the four corners and bending up the sides. Find the largest volume that such a box can have. 4) A farmer wants to fence an area of 750 000m^2 in a rectangular field and divide it in half with a fence parallel to one of the sides of the rectangle. How can this be done so as to minimize the cost of the fence? 5) Find the point on the line y = 5x + 4 , that is closest to the origin. 6) Find the point on the parabola 2y = x2 that is closest to the point ( 4,1). 7) A rectangle is inscribed in a semicircle of radius 2 cm. Find the largest area of such a rectangle. 8) Find the largest possible volume of a right circular cylinder that is inscribed in a sphere of radius "r". 9) Find the lengths of the sides of an isosceles triangle which has a perimeter of 12 m and a maximum area. 10) Find the dimensions and area of the largest rectangle having its two lower corners on the x-axis and its two upper corners on the parabola y = 16 x^2. 11) Find the volume of the largest open topped rectangular box that has a square base and a total surface area of 3600 cm^2