SOLUTION: The inventor of a new product believes that the cost of producing the product is given by the function C(x) = 1.75x + 7000 If the inventor charges $4 per unit, then her profit

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Question 62801This question is from textbook
: The inventor of a new product believes that the cost of producing the product is given by the function
C(x) = 1.75x + 7000
If the inventor charges $4 per unit, then her profit for producing and selling x units is given by the function P(x) = 2.25x - 7000
(a) What is her profit if she sells 2000 units?
(b) What is her profit if she sells 5000 units?
(c) What is the break-even point for sales?
 This question is from textbook

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The inventor of a new product believes that the cost of producing the product is given by the function
C(x) = 1.75x + 7000
If the inventor charges $4 per unit, then her profit for producing and selling x units is given by the function P(x) = 2.25x - 7000
(a) What is her profit if she sells 2000 units?
P(2000)=2.25(2000)-7000
P(2000)=4500-7000
P(2000)=-2500
That's not a profit, that's a loss.
:
(b) What is her profit if she sells 5000 units?
P(5000)=2.25(5000)-7000
P(5000)=11250-7000
P(5000)=4250
:
(c) What is the break-even point for sales?
P(x)=C(x)
2.25x-7000=1.75x+7000
2.25x-1.75x-7000=1.75x-1.75x+7000
.50x-7000=7000
.5x-7000+7000=7000+7000
.5x=14000
.5x/.5=14000/.5
x=28000
Happy Calculating!!!