Need help with #15 please. It is an Optimization Problem.

(b) Draw a diagram illustrating the general situation. figure, and bending up the Introduce notation and label the diagram with your the box is to have a double symbols. obtained by folding the si (c) Write an expression for the volume. that such a box can have. (d) Use the given information to write an equation that relates the variables. (e) Use part (d) to write the volume as a function of one variable. (f) Finish solving the problem and compare the answer with your estimate in part (a). 13. A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do 21. A rectangular storage conta this so as to minimize the cost of the fence? ume of 10 m'. The length of 14. A farmer has 1200 ft of fencing for enclosing a trapezoidal rial for the base costs $10 pe field along a river as shown. One of the parallel sides is three sides costs $6 per square me times longer than the other. No fencing is needed along the the least expensive such con river. Find the largest area the farmer can enclose. 22. Rework Exercise 21 assumin made from the same materia 39. 23. A package to be mailed using measure more than 108 inch the longest dimension and gi the package, perpendicular to 3x sions of the rectangular box ume that may be mailed. 15. A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared length with a neighbor who will split the cost of that portion of the fence. If the fencing costs $20 per linear foot to install and the farmer is not willing to spend more than $5000, find the dimensions for the plot that would enclose the most area 16. If the farmer in Exercise 15 wants to enclose 8000 square feet of land, what dimensions will minimize the cost of the 24. Refer to Exercise 23. Find the mailing tube of greatest volum fence ? US postal service. 17. (a) Show that of all the rectangles with a given area, the one with smallest perimeter is a square. 25. Find the point on the line y = (b) Show that of all the rectangles with a given perimeter, the origin. one with greatest area is a square. 26. Find the point on the curve y 18. A box with a square base and open top must have a volume of point (3, 0). 32,000 cm'. Find the dimensions of the box that minimize the 27. Find the points on the ellipse 4 amount of material used. away from the point (1, 0)