SOLUTION: A farmer decides to enclose a rectangular&#8203; garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 60 ft of&#

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Question 1058410: A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 60 ft of fence? What should the dimensions of the garden be to give this area?
And,
Total profit P is the difference between total revenue R and total cost C. Given the following total-revenue and total-cost functions, find the total profit, the maximum value of the total profit, and the value of x at which it occurs.
R(x)=1300x-(x-squared)
C(x)=3100+20x
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52756)   (Show Source):
You can put this solution on YOUR website!
.
See the lesson
    - A farmer planning to fence a rectangular area along the river to enclose the maximal area
in this site.

Very similar problem was solved there for you. It is precisely your case, your prototype, your sample.
Read it attentively and then solve your problem by substituting your data.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".

The other lessons under this topic are
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
    - A rectangle with a given perimeter which has the maximal area is a square
    - A farmer planning to fence a rectangular garden to enclose the maximal area
    - A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
Let = the length of the rectangle
Let = the width of the rectangle
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Use formula for perimeter of a rectangle

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Let = the area of the rectangle

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This is a parabola. To find the peak, use the
formula , where the
form is:
( )

-----------------------
Plug this result back into equation

ft2
--------------------------------

ft
The maximum area is a 15 x 15 square
--------------------------------------------

-----------------------------------

This is the expression for profit
-----------------------------------
Use formula for

Plug this value back into equation

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Here's the plot of the profit:

My numbers look close

SOLUTION: A farmer decides to enclose a rectangular&#8203; garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 60 ft of&#

SOLUTION: A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 60 ft of&#