Calculus rate of change problem?

Question

Can anyone solve this for me. I need detailed work, please.

Thanks!

We wish to construct a rectangular lot having an area of 550 square meters. The fencing to be used for 3 sides of the lot costs $4 per running meter. The front, being fancier, will cost $7 per running meter. Find the dimensions of the lot which will minimize the cost of the fencing.

Answer 1

Let x and y be lot dimensions.
xy = 550, so y = 550/x. Also,

c = 4(x + 2y) + 7x
c = 4x + 8y + 7x
c = 11x + 8(550/x)
c = 11x + 4400/x

cost minimizes when derivative = 0, so
c' = 11 - 4400/x² = 0
11x² = 4400
x² = 400
x = 20 m.
y = 550/20 = 27.5 m.