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» » » Thread: Having problem making a connection to plug into a Rectangle formula any Thoughts?
|Posted by 10615654 at Mar 4, 2010 12:10:55 PM|
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
|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?
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,
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.