23-optimization1

23-optimization1 - Math 1a Optimization Fall, 2009 1 (a)...

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Unformatted text preview: Math 1a Optimization Fall, 2009 1 (a) Suppose a rectangular region has fixed perimeter of 40 cm. What is the largest area the region can have? (b) Suppose now that the region was in the shape of a right triangle, not a rectangle. If the perimeter is still 40 cm, what is the largest area possible for the region? 2 A farmer has 250 feet of fencing and wishes to fence in a rectangular region against his barn. Thus one side of the rectangle will be the barn wall and the remaining three sides will require fencing. What is the largest rectangular area the farmer can enclose? 3 A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cut out of the corners, then the sides are folded up to create an open-top box. What size squares should be cut out so that the box has the largest possible volume? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................ . . . . . . . . . . . . . . . . . . . . . . . . . . .................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . ............................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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23-optimization1 - Math 1a Optimization Fall, 2009 1 (a)...

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