SOLUTION: Hello can anyone help solve this problem with work shown and answers it will help me learn how to do these problems for my upcoming test. Sean's Widget Company has revenue tha

Question 289772: Hello can anyone help solve this problem with work shown and answers it will help me learn how to do these problems for my upcoming test.

Sean's Widget Company has revenue that is modeled by the function R(x) = -4x2 + 35x and costs modeled by the function C(x) = 12x +30. The input variable x is in hundreds of widgets, and the outputs of the functions are in units of thousands of dollars. Construct a profit function P(x) and find the value of x that maximizes the profit.

Thank you John
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Sean's Widget Company has revenue that is modeled by the
function R(x) = -4x2 + 35x and costs modeled by the function C(x) = 12x +30.
The input variable x is in hundreds of widgets, and the outputs of the
functions are in units of thousands of dollars.
Construct a profit function P(x) and find the value of x that maximizes the profit.
:
Profit = Revenue - Cost
P(x) = R(x) - C(x)
Which is
P(x) = -4x^2 + 35x - (12x + 30)
Removing the bracket changes the signs
P(x) = -4x^2 + 35x - 12x - 30
Combine like terms
P(x) = -4x^2 + 23x - 30
:
A quadratic equation, we can find the axis of symmetry: x = -b/(2a)
That value of x will give us max profit
x =
x =
x = +2.875 hundreds of widgets
:
287.5 ~ 288 widgets for max profit (has to be an integer)
:
:
To find the actual profit value (in thousands), substitute 2.88 for x in the
equation P(x) = -4(2.88^2) + 23(2.88) - 30
RELATED QUESTIONS
Hello, I do not understand how to solve mutiplyins fractions with varibles. I am stuck (answered by sofiyac,ucangetbushra@hotmail.com)

solve and show all work please so I can learn how to do these problems... (answered by sudhanshu_kmr)

I'm having difficulty with this problem. -6(5X+2)=198 I was wondering if you could solve (answered by checkley71)

I am having so much trouble with this problem, and I need help. I have tried and... (answered by checkley71,stanbon)
In section 3-8. I need to know how to work out the problems. The computer will give the (answered by venugopalramana)
Please help me with this problem. I am confused and am trying to learn how to solve this... (answered by jim_thompson5910,stanbon)
Hello out there,I need help with only one problem that gives me different... (answered by Nate)
i am in desperate need of some help...i do not understand how to do this it confuses... (answered by venugopalramana)
I need help to learn how to set up equations so that I can solve it; Because I am having... (answered by rfer)