Rectangular Garden Math Problem?

A landscape architect plans to enclose a 3900 square foot rectangular region in a botanical garden. She will use shrubs costing 21 dollars per foot along three sides and fencing costing 10 dollars per foot along the fourth side. The goal is to find the minimum total cost.





a. First express the cost c(x) in terms of x, the length of the side with fencing.





b. Next give the minimum value of the cost function c(x):





For a, i got C= 10x+21y^3 but i don't know how to put it in terms of x. I know that for b you just take the derivative and find the minimum but i'm having trouble getting part a.

Rectangular Garden Math Problem?
okay





x is the side with the fencing





it's a rectangle.





one of the other sides is also x





the area is 3900





so the other two sides are 3900/x





so, the real equation is





c(x) = 10x + 21(x + 2(3900/x))





taking the derivative d(function), we get:





c'(x) = d(10x) + d(21x) + d(42(3900/x))





c'(x) = 10 + 21 + (42*3900)x^-2





Set this to zero and solve for x.





Hope that helps.
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