6. Let a and b two positive numbers with 8a + 50 =40 . Find the maximum value for their product, ab.7. OBC is a right triangle with right angle C. This triangle's base is on the positive x-axis; the vertex O is at the origin, and the vertex C is on the positive x-axis. The vertex B is on the line y+2x =10 . Find the maximum area of this triangle. Draw a diagram first.8. A box with a square base and closed top has a fixed surface area of 60 cm . Find the dimensions of the box that give the maximum volume.9. An open box to be formed from a piece of metal 16 by 30 inches by cutting out squares of equal sides from the corners and bending up the sides. What size square should be cut out to create a box of greatest volume? What is the maximum volume