SOLUTION: 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, t

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Question 1058415: 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)= 1000x-(x squared)
C(x)= 3400+10x

And,

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 32 ft of​ fence? What should the dimensions of the garden be to give this​ area?


Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Regarding your second question, 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


Do not put more than one question into your future posts.