4. Find the minimum sum of two numbers whose product is 500. 5. Find the maximum sum of two numbers whose product is 500. 6. Find the maximum sum of two numbers, each of which is in [0, 300 whose product is 500. 7. Find the maximal area of a right triangle with hypotenuse of length 1 8. A rancher has 1000 feet of fencing in which to construct adjacent, equally sized rectangular pens. What dimensions should these pens have to maximize the enclosed area? 15 9. Astandard soda can is roughly cylindrical and holds 355cm of liquid. What dimensions should the cylinder be to min- imize the material needed to produce the can? Based on your dimensions, determine whether or not the standard can is produced to minimize the material costs. 10. Find the dimensions of a cylindrical can with a volume of 206in that minimizes the surface area The "#10 can"is a standard sized can used by the restau- rant industry that holds about 206in with a diameter of 6 2/16in and height of 7in. Does it seem these dimensions where chosen with minimization in mind? 11. The United States Postal Service charges more for boxes whose combined length and girth exceeds 108" (the length" of a package is the length of its longest side; the 1 girth is the perimeter of the cross section, i.e., 2w +2h).