If the garden is to be 2450 square feet, and the fence along the driveway costs $6 per foot while on the other three sides it costs only $2 per foot, find the dimensions that will minimize the cost.

Question

Mathematics

Emma Pennington

13 April, 09:57

If the garden is to be 2450 square feet, and the fence along the driveway costs $6 per foot while on the other three sides it costs only $2 per foot, find the dimensions that will minimize the cost.

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Answers (1)

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Azul Collins · Answer 1

Cost (C) = 8x + 4y

For minimum cost C' = 0

8 + 4dy/dx = 0

dy/dx = - 2

d (xy) / dx

xdy/dx + y

dy/dx = - y/x = - 2

y = 2x

x (2x) = 2450

2x^2 = 2450

x^2 = 1225

x = √1225 = 35

y = 2 (35) = 70

Therefroe for minimum cost the dimension of the graden should be 35 by 70 feet.