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Pre-Calc Homework Solutions 157

Pre-Calc Homework Solutions 157 - Section 4.4 12(a Note...

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12. (a) Note that x 2 y 5 1125, so y 5 } 11 x 2 2 5 } . Then c 5 5( x 2 1 4 xy ) 1 10 xy 5 5 x 2 1 30 xy 5 5 x 2 1 30 x 1 } 11 x 2 2 5 } 2 5 5 x 2 1 33,750 x 2 1 } d d c x } 5 10 x 2 33,750 x 2 2 5 } 10( x 3 2 x 2 3375) } The critical point occurs at x 5 15. Since } d d c x } , 0 for 0 , x , 15 and } d d c x } . 0 for x . 15, the critical point corresponds to the minimum cost. The values of x and y are x 5 15 ft and y 5 5 ft. (b) The material for the tank costs 5 dollars/sq ft and the excavation charge is 10 dollars for each square foot of the cross-sectional area of one wall of the hole. 13. Let x be the height in inches of the printed area. Then the width of the printed area is } 5 x 0 } in. and the overall dimensions are x 1 8 in. by } 5 x 0 } 1 4 in. The amount of paper used is A ( x ) 5 ( x 1 8) 1 } 5 x 0 } 1 4 2 5 4 x 1 82 1 } 40 x 0 } in 2 . Then A 9 ( x ) 5 4 2 400 x 2 2 5 } 4( x 2 2 x 2 100) } and the critical point (for x . 0) occurs at x 5 10. Since A 9 ( x ) , 0 for 0 , x , 10 and A 9 ( x ) . 0 for x . 10, the critical point corresponds to the minimum amount of paper. Using x 1 8 and } 5 x 0 } 1 4 for x 5 10, the overall dimensions are 18 in. high by 9 in. wide.
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