need help with these

1. length 20, width 5 2. length 10, width 3. length 5. width = 5 4. length 10. width = 10 5. length 20. width = 10 6. length 5, width 10A rectangular box with no top and two parallel partitions is to be constructed. The box is to have a volume of 125 cubic inches. (i) Determine the amount A of material needed to construct the box in terms of the length x and width y of the box (assume no material is wasted). 250 500 1. A(x, y) = xy + y 250 500 2. A(x, y) - 2xy + y 250 250 3. A(x, y) = ry + ac 250 500 4. A(x, y) - xy + y 500 500 5. A(x, y) - ry + y(ii) Find the dimensions of the box that will require the least amount of material to be used in its construction. 1. length = 20, width 2. length = 10, width - 5 3. length = 5, width = 5 4. length = 10, width 10 5. length = 20, width 10Use Lagrange multipliers to find the shortest distance from the point (5.1,3) to the plane 5x + 10y - 42 - 2. 1. 47 7V141 2. 47 3. 2V141 4. V141 47V141 5. 7Find the points on the surface 2 =CV -+ 25 that are closest to the origin. 1. (0, 0, -5), (0, 0, 5) 2. (4, -4, 3), (-4, 4, -3)Use Lagrange multipliers to find the volume of the largest rectangular box in the first oc- tant with three faces in the coordinate planes and one vertex in the plane 3x + y + 4z = 9. 1. volume 001 0 10 2. volume = 3. volume = 6 4. volume 5. volume