Question 1201028: For a certain company, the cost for producing x
items is 45x+300
and the revenue for selling x
items is 85x−0.5x^2
.
The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x
items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x
that will create a profit of $300
.
x= ?
Part c: Is it possible for the company to make a profit of $15,000
?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
For a certain company, the cost for producing x items is 45x+300
the revenue for selling x items is 85x−0.5x^2
Profit = Revenue - Cst
P = 85x−0.5x^2 -(45x+300)
P = -0.5x^2 +40x -300 ...........................(a)
If Profit =300
300 =-0.5x^2 +40x -300
-0.5x^2 +40x -600=0
solve the equation
Multiply by -10
5x^2-400x+6000=0
divide by 5
x^2 -80x+1200 =0
(x-20)(x-60)=0
x= 20 or 60........................(b)
P = -0.5x^2 +40x -300
if profit has to be 3500
3500 =-0.5x^2 +40x -300
-0.5x^2 +40x -3800=0On solving the equation the roots are not real ( They are complex)
This profit is not possible........................(c)
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