word problem

[rachael724]

A rancher has 192 feet of fencing. Using this for three sides of a rectangular corral where the fourth side will be a river with a straight shore, what is the maximum number of square feet of corral space that she can expect?


can someone help me?

 

[Unco]

G'day.

            x
    ______________
    |             | |
    |              \ \
  y |               | | river            
    |              / /
    |_____________| |

            x
  
 Perimeter = x + x + y = 2x + y

 She has 192 feet of fencing for the perimeter:

     192 = 2x + y      [1]

  The area to be maximised is given by 
     
      A = xy   [2]

 Make x or y the subject of [1] and subsitute this into [2].

 Differentiate to get A'=....

 Set A' = 0, and solve for your varible.

 See how you go.

Edit: Corrected 193 instead of 192.

 

[rachael724]

7200?

 

[stapel]

7200?

How does this relate to the exercise?

Please reply in complete sentences, showing your reasoning, as modelled by the tutor, so we can understand what you are saying. Thank you.

Eliz.

 

[rachael724]

is that the answer?

 

[Unco]

Unfortunately, that is not the maximum area. Please show you work so we may be of better help.

 

[Guest]

Two equations as shown by previous postings...

192 =2x + y

and

Area =xy

rearrange the first equation...
y = 192-2x

and sub this into the second equation.

A= x(192-2x)
A= 192x - 2x^2

The max. area is found by doing the first and second differential of this equation.

dA/dx = 192 -4x

now keep going and solve this for when dA/dx =0 and find the x value.