Calculus Minimum Cost Quesion:?

A landscape architecht plans to enclose a 3000 square foot rectangular region in a botanical garden. She will use shrubs costing $25 per foot along three sides and fencing costing $10 per square foot along the fourth side. Find the minimum total cost, show all work.





Thanks!

Calculus Minimum Cost Quesion:?
Use s for the length of the side which will be used for fencing. The area of 3000 must come from s times the other length so this length must be 3000/s.


The cost C will be 10s for the fencing side + 25s for the side opposite + 25*(3000/s) for each of the other sides so


C = 35s + 50*(3000/s) ----(A).


You need to differentiate this and put it equal to zero. Solve the resulting equation to find the value of s which minimises the cost. Then put this value of s back into the cost function at A to find the actual minimum cost.


Your final answer should be between $4500 and $4600