Section 4.7-solutions

# Section 4.7-solutions - to(aqt73 – Section 4.7 –...

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Unformatted text preview: to (aqt73) – Section 4.7 – isaacson – (55826) 1 This print-out should have 4 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A rectangular dog pound with three kennels as shown in the figure consists of a rectangular fenced area divided by two partitions. Determine the maximum possible area of this pound if 16 yards of chain link fencing is available for its construction. 1. max area = 9 sq.yards 2. max area = 6 sq.yards 3. max area = 10 sq.yards 4. max area = 7 sq.yards 5. max area = 8 sq.yards correct Explanation: Let the dimensions of the floor of the dog pound be as shown in the figure below x y Then the area of the pound is given by A = xy , while the total fencing needed is the sum of the perimeter 2 x +2 y and the inner partitions 2 y . Since 16 yards of fencing available we get a relation 16 = 2 x + 4 y i.e. , 8 = x + 2 y . Eliminating y from these two equations gives an expression A = 1 2 x (8- x ) = 4 x- 1 2 x 2 for the area solely as a function of x . As the maximum value of x is x = 8, the maximum area will thus be the absolute maximum value of A on the interval [0 , 8]. This maximum will8]....
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Section 4.7-solutions - to(aqt73 – Section 4.7 –...

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