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5.4

Optimization. 5.4. A box with a square base and open top must have a volume of 32,000 cubic cm. Find the dimensions of the box that minimize the amount of material used. 40 by 40 by 20. Find two numbers whose sum is 40 and whose product is as large as possible. 20 and 20.

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5.4

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  1. Optimization 5.4

  2. A box with a square base and open top must have a volume of 32,000 cubic cm. Find the dimensions of the box that minimize the amount of material used. 40 by 40 by 20

  3. Find two numbers whose sum is 40 and whose product is as large as possible. 20 and 20 What is the smallest perimeter possible for a rectangle whose area is 25 square inches? P=20

  4. The top and bottom margins of a poster are each 2 cm and the side margins are each 1 cm. If the area of printed material on the poster is fixed at 92 sq. cm, find the dimensions of the poster with the smallest area.

  5. An advertisement consists of a rectangular printed region plus 1-in margins on the sides and 1.5-in margins at the top and bottom. If the total area of the advertisement is to be 120 sq in, what dimensions should the advertisement be to maximize the are of the printed region?

  6. A two-pen corral is to be built. The outline of the corral forms two identical adjoining rectangles. If there is 120 ft of fencing available, what dimensions of the corral will maximize the enclosed area?

  7. What dimensions for a one liter cylindrical can will use the least amount of material? Motor Oil We can minimize the material by minimizing the area. We need another equation that relates r and h: area of ends lateral area

  8. What dimensions for a one liter cylindrical can will use the least amount of material? area of ends lateral area

  9. What are the dimensions of the largest rectangle that can be inscribed in the ellipse ?

  10. Homework pg 214 #2,5,6,21(calc)

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