C2 - Applications of Diffrentiation

hey guys

i am really boggled by this question, i only have half of the answer and i dont know how to get the other half:

Question:

A rectangular sheep pen is to made out of 1000m of fencing, using an existing straight hedge for one of the sides. Find the maximum area possible, and the dimensions neccessary to achieve this

v much appreciated! :smile:

frm hatty341

Reply 1

Simba

16

hatty341

hey guys

i am really boggled by this question, i only have half of the answer and i dont know how to get the other half:

Question:

A rectangular sheep pen is to made out of 1000m of fencing, using an existing straight hedge for one of the sides. Find the maximum area possible, and the dimensions neccessary to achieve this

v much appreciated! :smile:

frm hatty341

Let the length of the sides perpendicular to the hedge be 'x', and let the length of the side parallel to the hedge be 'y'.

2x + y = 1000

y = 1000 - 2x

Area of enclosure = xy = x(1000 - 2x) = -2x² + 1000x

dA/dx = -4x + 1000 = 0

x = 250

=> y = 500

Therefore, the dimensions required are 500 metres by 250 metres. The maximum area therefore is 500 metres * 250 metres = 125000m²

Hope this helps,

~~Simba

Reply 2

latentcorpse

12

the hedge means fencing is only used on one side so it's x+y=1000 not 2x+y

Reply 3

Simba

16

latentcorpse

the hedge means fencing is only used on one side so it's x+y=1000 not 2x+y

No, that's wrong... otherwise it wouldn't be a rectangular enclosure...

You're saying 1 side = hedge, 1 side = x, and 1 side = y. That's only 3 sides :wink:

...

C2 - Applications of Diffrentiation

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