Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

The management of a department store has decided to enclose an 800 sq. ft.area outside the building for displaying potted plants and flowers. One side willbe formed by the exterior wall of the store, two sides will be constructed of pineboards, and the fourth side that is opposite to the wall will be made of galvanizedsteel fencing. If the pine board fencing costs $6/ft. and thesteel fencing costs $3/ft,determine the dimensions of the enclosure that can be erected at minimum cost

Sagot :

Answer:

Dimension of the enclosure is 56.56 ft * 14.14 ft

Step-by-step explanation:

Given -

Let us suppose that x is the length of steel fence and y is the length of one side of pine boards

 

We know that - xy = 800.

y = 800/x

 

Let us say that  C is the cost of fence

 

                = 3x + 6(2y) = 3x + 12y = 3x + 12(800/x)

 

C = 3x + 9600x-1, x > 0

 

C' = 3 - 9600x-2 = (3x2-9600)/x2

 

C' = 0 when 3x2 = 9600

 

                  x2 = 3200

 

                  x = √3200 ft ≈ 56.56 ft

So, the cost is minimized when x ≈ 56.56 ft and y = 800/x ≈ 14.14 ft

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.