points Previous Answers SProCalc7 31.050. A farmer has 2400 ft of fencing and wa
ID: 3014584 • Letter: P
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points Previous Answers SProCalc7 31.050. A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He does not need fence along the river (see the figure). What are the dimensions of the fleld of largest area that he can fence? (a) Experiment with the problem by drawing several diagrams illustrating the situation. Calculate the area of each configuration, and use your results to estimate the dimensions of the largest possible field. (Enter your answers as a comma separated list.) (b) Find a function that models the area of the field in terms of one of its sides. (c) use your model to solve the problem, and compare with your answer to part (a). Maximum area occurs at the following values. smaller dimension larger dimension 1200 MacBooExplanation / Answer
3]
2x + y = 2400
A = xy = x[2400 - 2x]
=> A(x) = - 2x2 + 2400x
using this one can solve for x and y
x = 600 ft and y = 1200 ft
4]
2[x + y] = 750
A = xy = x[375 - x] = 375x - x2
differentiate this with respect to x.
A' = 375 - 2x
equate it to zero for maxima
x = 375/2 = 187.5 ft
for this, A = 375(187.5) - (187.5)2 = 35156.25 sq ft
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