Stuffed Sheets.com - Maxima and Minima Word Problems

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(C-D-MM-1) A farmer has 1,000 feet of fencing available with which to construct a rectangular enclosure along one side of a barn. Assuming that no fencing is needed along the barn, what are the dimensions of the rectangle of greatest area? ($1.25)

(C-D-MM-2) Find the point of the curvewhere the slope of the tangent line is minimized. ($1.25)

(C-D-MM-3) Find the dimensions of a rectangle whose area is 300 square feet and has minimum perimeter. ($1.25)
(C-D-MM-4) A square sheet of metal 16 inches on a side is to be made into a box, by cutting out an equal-size square from each corner then folding up the four sides. Find the dimensions of the box of largest volume. ($1.25)

(C-D-MM-5) The sum of the cubes of two numbers is a minimum. Find the numbers if their sum is 12. ($1.25)
(C-D-MM-6) Find the coordinates of the points on the curvewhich are nearest to the point ($1.25)

(C-D-MM-7) Find the points on the circlethe sum of whose distances fromandare minimized. ($1.25)

(C-D-MM-8) Find the point C on the x-axis the sum of whose distances fromandis a minimum. ($1.25)
(C-D-MM-9) What is the maximum possible area of an isosceles triangle which has two sides of length k. ($1.25)
(C-D-MM-10) A wire 10 inches long is cut into two pieces. One piece is bent into a square and the other into an equilateral triangle. What would the perimeter of each figure be if the sum of the areas is minimized? ($1.25)

(C-D-MM-11) A Norman window consists of a rectangular shape surmounted by a semi-circular one. If the perimeter of the window is 38 feet, what are the height of the rectangular section and radius of the semi-circle that maximize the area? ($1.25)

(C-D-MM-12) Find the dimensions of the rectangle of maximum perimeter that has two vertices on the curveand sits on the x-axis. ($1.25)
(C-D-MM-13) Find the minimum value ofsubject to the condition ($1.25)
(C-D-MM-14) Find the dimensions of the rectangle whose sides are parallel to the axes, is inscribed in the ellipseand has maximum perimeter. ($1.25)
(C-D-MM-15) If m and n are positive constants, x and y are positive variables, find values for x and y that maximize the productsubject to the condition ($1.25)
(C-D-MM-16) What is the volume of the largest right circular cone that can be inscribed in a sphere of radius 10 inches? ($1.25)
(C-D-MM-17) A fence 8 feet high is one foot from the side of a building. What is the length of the shortest ladder that will reach over the fence and touch the building? ($1.25)

(C-D-MM-18) An urn is to be constructed of 18K gold in the shape of a triangular cylinder, with base and top equilateral triangles. If the volume is to be 400 cubic centimeters, what dimensions will minimize the amount of gold used? ($1.25)

(C-D-MM-19) Two towers 60 feet apart are 50 feet and 30 feet high respectively. The top of each tower is attached to a guy wire, anchored by a stake in the ground between them. Where should the stake be placed so that the length of the wire is minimized? ($1.25)

(C-D-MM-20) What is the length of the longest pipe which can be pulled horizontally (on a dolly) around a corner from a tunnel 10 feet wide to one 3 feet wide if the tunnels meet at right angles. ($1.25)
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