WebGraphing.com Forum - Print Post -

WebGraphing.com Forum
» List all forums
» » Forum: Precalculus and Trigonometry Homework Help
» » » Thread: Having problem making a connection to plug into a Rectangle formula any Thoughts?
» » » » Post: Re: Having problem making a connection to plug into a Rectangle formula any Thoughts?

Print at May 18, 2013 10:33:40 AM

Posted by pskinner at Mar 4, 2010 12:23:16 PM

Re: Having problem making a connection to plug into a Rectangle formula any Thoughts?

A rectangular garden next to a building is to be fenced on three sides. Fencing for the side parallel to the building costs $60 per foot, and material for the other two sides costs $40 per foot. If $2,300 is to be spent on fencing, what are the dimensions of the garden with the largest possible area?

My cost formula = 2300 = 2(40x) +60y

I know Area = xy

But i have no idea how to combine these two equations to create a single variable equation to find Largest possible area with A=xy

Any thoughts?

Great question! You have all the formulas correct. In order to solve this, you need to use some calculus. The area is a function of both x and y, while y is a function of x. So,

A'(x)=d/dx(x*y)=xy'+y

Set A'(x)=0 to find the value of x for which this area is a maximum, so xy'+y=0. Further, you can use your cost formula to solve for y and substitute that back into this last equation. Also, you can calculate y' since it is the slope of the cost curve which is a line. That will enable you to get x, and in turn, y.

Without calculus, I would have no idea how to solve this.
----------------------------------------
Principal Skinner