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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? |
| Posted by 10615654 at Mar 4, 2010 12:10:55 PM |
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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? |
| 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, 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 |