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 The cost of 2000 units of her invention is $10,500.

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Question 70361: The inventor of a new product believes that the cost of producing the product is given by the function: C(x)= 1.75x + 7000
The cost of 2000 units of her invention is $10,500.
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?
Found 2 solutions by funmath, bucky:
Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website!
There's a missing variable in your cost function. Can you check what you typed in against what you're trying to solve? I thought I might be able to figure out what it was supposed to be, but it didn't check out with the other information you typed in.

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
From the way this problem is worded, the equation for C(x) is not needed to answer the questions
that are asked. The only equation that applies is:
.

The first question ... What is the profit if she sells 2000 units? Calculate the profit by
setting x equal to 2000 units so that the equation becomes:
.

.
The negative sign tells you that overall she loses $2500 if she sells only 2000 units.
.
The second question ... What is the profit if she sells 5000 units? Do the same calculation
as above, but this time set x equal to 5000 units so that the equation becomes:
.

.
The positive answer tells you that overall she makes $4,250 if she sells 5000 units.
.
So somewhere between sales of 2000 units (a loss) and selling 5000 units (a gain) she
reach a break-even point. At that break-even point her profit would be zero (neither a
loss nor a gain). So this time set the profit equal to zero in the equation and solve the
resulting equation for x.
.

.
Add 7000 to both sides and transpose the equation:
.

.
Divide both sides by 2.25 to get:
.
}
.
This result tells you that if she sells less than this amount she loses money, but if
she sells more than this number of units she makes money. Therefore, you can say that
she loses a very small amount of money if she sells 3111 units, and she makes a very small
amount of money if she sells 3112 units.
.
Hope this helps you to see your way through the problem ... especially with regarding
the information on the costs involved with production, C(x), and the sales price of $4.00
per unit. That information was not needed because you were provided with an
equation that
directly calculates profit based on the number of units sold.