Need help with word problem please. Work already done but incorrect answer.

Question

anonymous · Answer

attachment

anonymous · Answer

If the area of a fence is the expression $$A=xy$$

The perimeter of the fence is the expression $$P = 2x + 2y$$
The farmer only has 1600 yards of fencing. 

so thus $$1600 = 2x + 2y $$

Now If we can solve for a expression say solve for y. 
$$2 y = 1600 - 2x  $$$$y = 800 - x $$

Now we can see that we know x. Let us substitute it for the expression of Area. $$Area= x(800-x)$$

Solve$$A = 800x-x^{2}$$

Since we want the max area take he first derivative at the max. and solve for 0 where the slope of the critical value $$A' = 800 - 2x$$at max is 0. 

$$0 = 800 - 2x$$

Now solve for x $$x = 400$$

Now we have our x dimension let us find the y dimension. 

$$y = 800-x$$

$$y = 400$$

We want to know what dimensions will give the maximum area for the three plots. 
$$(\frac{ 400 }{ 3 }, \frac{ 400 }{ 3 })$$

anonymous · Answer

If you want just the maximum rectangular area it is 400 by 400

anonymous · Answer

Not sure how derivatives work yet. I typed in 400 for the larger value but smaller value was not 400.

anonymous · Answer

The smaller value is the y direction ?

anonymous · Answer

doesnt say just says enter small value and larger value

anonymous · Answer

Well perhaps the expression for the perimeter is 

1600 = 2x + 4y

2x = 1600 -4y

x = 800 - 2y

A= (800-2y)(y)

A = 800y - 2y^2

A' = 800 -4y

y = 200

and 

then 

x = 800 - 2(200)

x = 400

so either way .. weird.  

try 400 and 200

anonymous · Answer

This is the example given in the lesson. Which is the exact same problem just a different total. 

200 was correct, but if you see mine above I solved it the exact same way but got the wrong values. The only difference from what you solved and what I solved is that you solved for x and I solved for Y.

Why would that make a difference in the end answers? Did I mess up on my math above?

anonymous · Answer

You made a mistake in your arithmetic

the quantity 

$$2x + 4y = 1600$$ 

does not divide into $$2x + y \neq  400$$

You cant do that.

anonymous · Answer

ah yes it would be

1/2x+y=400

but it is better to solve for x to sway away from the fractions

anonymous · Answer

yes.

anonymous · Answer

Thank you

anonymous · Answer

yw =))