An 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?
I know how to work a and b, but how do I work c?
break even is when Profit is zero. Revenue is equal to costs at that point.
So if Profit is zero, then 0=2.25x-7000, and you can solve for x.
To calculate the break-even point, we set the profit function equal to zero and solve for x:
0 = 2.25x - 7000
To solve for x, we isolate it on one side of the equation:
2.25x = 7000
Divide both sides of the equation by 2.25:
x = 7000 / 2.25
Using a calculator, we find that x ≈ 3111.11.
Therefore, the break-even point for sales is approximately 3111 units.