I don't get it, my answers are wrong

Question

A rectangular field is to be subdivided in 4 equal fields. There is 4450 feet of fencing available. 


Find the dimensions of the field that maximizes the total area. (List the longer side first) 
Width =  feet Length =  feet 
What is the maximum area ? Area = 

 

My answers are wrong

 

 

The revenue R in dollars, derived from selling x picture frames is given by

How many items should be sold to maximize the revenue?  
What is the revenue? 

Answer 1

A rectangular field is to be subdivided in 4 equal fields.

Let the  length of an smaller rectangle is x 

Let the width of an smaller rectangle is y

From  the above figure the perimeter rectangle is  6(x+y)

Total available fencing is  4450 feet

6(x+y) = 4450

x+y = 4450/6

x+y = 741.667

y = 741.667 -x

So the area of smaller rectangle is length * width

a = x * (741.667 -x)

a = 741.667x - x²

Total area A = 4*a

A = 4(741.667x - x²)

To Maximize the total area , we need to equate the first derivative to zero for finding the dimensions

A'= [4(741.667x - x²)]' = 0

741.667 - 2x = 0

2x = 741.667

x = 370.83

Now find for y

y = 741.667 - 370.83

y = 370.83

Length and width of smaller rectangle is 370.83 and 370.83

Length  of total rectangle is 370.83*2 =741.667

Width  of total rectangle is 370.83*2 =741.667

So the rectangle that has the most area for the shortest perimeter is a square .

Maximum area of smaller rectangle is = 370.83 * 370.83

                                                            =137517.48

So the total maximum area is = 741.667 * 741.667

                                               = 550069.92 

 Total maximum area is 550069.92  square feet

Answer 2

(2)

The revenue ( R ) in dollars given by R = -13x² + 49400x +2300

To maximize the revenue , we need to equate the first derivative to zero for finding the number of items sold 

R = -13x² + 49400x +2300

Apply derivative

R' = -26x +49400 =0

26x =49400 

x = 1900

So to get maximum revenue he need to sold 1900 items 

Maximum revenue = -13(1900)² + 49400(1900) +2300

                              = -46930000 +93860000 +2300

                             = 46932300

The maximum revenue is 46932300