Word problem

Question

You wish to build a rectangular pen facing north-south and east-west. there will be one north-south interior fence from the southern border to the northern border. the north-south fence costs $3 per linear foot and the east-west fence costs $1 per foot. you have $180 to spend on fence. what is the maximum area on square feet you can enclose for this price

Answer 1

I am not quite able to draw a picture of what we are building in this problem. Still, we could try and solve it. 

 

We need 2 sides - one is x-feet long and the other is y-feet long. Is that correct? We are not building all 4 sides in my solution. The x-feet wall cost 1 dollar per foot and all together it is 1x dollars.

 

The y-feet wall cost 3 dollars per foot, so all together it is 3y dollars. All together it cost 180 dollars, so, x+3y=180.

 

or y=(180-x)/3

 

Next step is to have the area formula. The area is A(x)=y*x=(180-x)/3*x. 

 

Next step is to simplify the equation and you have A(x)= 60x-x^2/3.

Next step is to derive A(x) and set the derivative to 0.

And solve that for x.

And then you will need to find y from the formula y=(180-x)/3 and the area.

 

Could you do that? Do you need more help?