Tough Calculus Problem.?

A landscape architect plans to enclose a 1300 square foot rectangular region in a botanical garden. She will use shrubs costing $25 per foot along three sides and fencing costing $10 per foot along the north side.





(a) If x is the length of fencing used, write a formula for the total cost in terms of x only.


C(x) =





(b) Find the length of fence that will minimize the total cost.


x = feet





(c) Find the minimum total cost. Give your answer to the nearest penny


15 minutes ago - 3 days left to answer.


Report It

Tough Calculus Problem.?
If x is the length of the north side, it must be the length of the south side. Moreover, the length of the east and west sides is 1300/x.





So, for A, you have (10+25)x + (25*2)(1300/x) as the cost. Simplifying, Cost=35 x + 65000/x.


We can then take the derivitive d(Cost)/dx =


35 - 65000/ x^2. We set this = to zero, and x is then sqrt (65000/35), which is about 43-44 ft.





Once you have minimum x, solve the C(x) equation for that value.
Reply:(a) C(x) = 10 x + 25*(x+2*1300/x)





(b) Since x %26gt; 0, let's minimize C(x) for x%26gt;0.


dC/dx = 10+25*(1-2*1300/x^2) = 35 -65000/x^2


dC/dx =0 or x^2 = 65000/35 = 13000/7


Thus, x = sqrt(13000/7) = 43.09 feet for minimum cost.





(c) minimum cost = C(sqrt(13000/7)) = $ 3016.62.