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1. Find the directions of a rectangle with perimeter 108 m whose area Is as large as possible. (If both values are the same number, enter it into both blanks.)
2. Find the dimensions of a rectangle area 1000 m^2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)
3. If 30,000 cm^2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box?
4. A box with a square base and open top must have a volume of 62,500 cm^3. Find the dimensions of the box that minimize the amount of material used.
5. Find the point on the line y = 5x + 4 that is closest to the origin.
6. A norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
7. A piece of wire 30m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.
8. A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. What is the length of the shortest ladder that will reach the ground over the fence to the wall of the building? (Round your answer to two decimal places.
9. A cone-shaped paper drinking cup is made to hold 30 cm^3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.)
10. A manufacturer has been selling 1000 flat-screen TVs a week at $350 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of TVs sold will increase by 100 each week.
11. A piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.