SOLUTION: I would like to ask a business and finance applcation involving functions. The inventor of a new product believes that the cost of producing the prodict is given by the function,

Question 81604This question is from textbook beginners algebra
: I would like to ask a business and finance applcation involving functions.
The inventor of a new product believes that the cost of producing the prodict is given by the function, example;
C(x)=1.75+7000
How much does it cost to produce 2000 units of her invention?
If the inventor in exercise 53 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 isf she sells 2000 units?
b.) What is her profit if she selss 5000 units?
C.)What is the break-even point for sales?
Please help
This question is from textbook beginners algebra

Answer by scott8148(5880) (Show Source):
You can put this solution on YOUR website!
the cost to produce 2000 units is found by setting x equal to 2000 in the cost function

C(2000)=1.75(2000)+7000 ... C=3500+7000 ... C=10500

the profit on x units is found by substituting the value of x into the profit function

a.) P(2000)=2.25(2000)-7000 ... P=4500-7000 ... P=-2500

b.) P(5000)=2.25(5000)-7000 ... P=11250-7000 ... P=4250

C.) the break even point is where there is no profit or loss ... find by setting P(x) equal to zero and solving for x

0=2.25(x)-7000 ... 7000=2.25x ... x=28000/9 ... this is not an integer value, so the break even point is between 3111 and 3112