Bob wants to create two pens. One pen if for a garden and it needs a heavy duty fence to keep out the critters. This heavy duty fence costs $15 per foot. The dog pen shares a side with the garden and has a lighter weight fence on the other three sides that costs $5 per foot. If each pen is to have an area of 504, find the values of x and y that would minimize the total cost of the fencing.

Question

Mathematics

Adolfo Compton

18 December, 17:42

Bob wants to create two pens. One pen if for a garden and it needs a heavy duty fence to keep out the critters. This heavy duty fence costs $15 per foot. The dog pen shares a side with the garden and has a lighter weight fence on the other three sides that costs $5 per foot. If each pen is to have an area of 504, find the values of x and y that would minimize the total cost of the fencing.

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Answers (1)

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Yazmin Glass · Answer 1

X y = 504

y = 504 / x

The total cost of fencing:

C (x) = 2 x * 15 + 2 y * 15 + 2 x * 5 + y * 5 =

= 30 x + 30 y + 10 x + 5 y = 40 x + 35 y = 40 x + 35 * 504 / x =

= 40 x + 17,640 / x

C' (x) = 40 - 17,640 / x²

40 - 17,640 / x² = 0

x² = 17,640 : 40

x² = 441

x = √441

x = 21 ft

y = 504 : 21

y = 24 ft