Optimization of Rectangle A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing \$50 per foot and on the other three sides by a metal fence costing \$10 per foot. If the area is 24 square feet, what are the dimensions of the garden that minimize the cost? (Let x= side with bricks; y= adjacent side)
I tried finding the length of one side as 24/x and the other as 24/y, but it 
hasn't gotten me far. I also thought about finding the variables through the perimeter, but I realized all they gave was the area.
Thank you!

First you have to know that the Area will equal x times y.
A=xy
You know the area is 24 square feet, so you can plug that in for A.
24=xy
From here you solve for y and it is y=42/x
Now you need to figure out a formula to find the cost to build this rectangular garden. 
The formula is C(x)= 50x + 10(x+2y)
The formula represents one side which is $50 and three sides worth $10 each. You have one x side left over and the 2y sides left. You add them because it's for perimeter. 
Next you distribute out the equation and will get C(x)=50x + 10x +20y which will equal 60x + 20y. 
You have what y equals, so you plug that into the equation. Your new equation will look like C(x)= 60x + 20(42/x). Now you have only one variable in the equation. You can distribute more and your new equation is
C(x)= 60x + (840/x)
To solve for x you have to take the derivative of that. The derivative is
C'(x)= 60 - (840/x^2). To solve for x you set it equal to zero. When you solve for x you get square root of 14. That is your x value and to solve for y you plug the square root of 14 into y=42/x. 
