Suppose the revenue from producing and selling x units of a given product is given by R(x)=10x-0.02x^2
a) Find the number of units produced if the revenue is $800.
I really need help with this, I don't know what to do?
just set R(x) = 800
800 = 10x - .02x^2
.02x^2 - 10x + 800 = 0
using the quad formula
x = (10 ± √36)/.04 , ahhh it would have factored
= (10 ± 6)/.04
= 400 or 100 units
The answer that I have to this question is 1000 units, I am confused.
sub in your answer
R(1000) = 10(1000) - .02(1000)^2 = -10 000
my answers
R(400) = 10(400) - .02(400)^2 = 800
R(100) = 10(100) - .02(100)^2 = 800
Why are you confused?
how did you possible get 1000?
I know I am getting the answer as you did, but the solution that I have with the question that says 1000
To find the number of units produced when the revenue is $800, you need to solve the equation R(x) = 800, where R(x) is the revenue function.
The revenue function is given as R(x) = 10x - 0.02x^2. To solve the equation R(x) = 800, substitute 800 in place of R(x):
10x - 0.02x^2 = 800
To solve this quadratic equation, you need to bring the equation to the standard quadratic form (ax^2 + bx + c = 0). Rearrange the equation:
0.02x^2 - 10x + 800 = 0
Since the coefficient of x^2 is a decimal (0.02), it may be helpful to multiply the equation by 100 to eliminate the decimal:
2x^2 - 100x + 80000 = 0
Now, you can solve this quadratic equation through factoring, completing the square, or using the quadratic formula. Let's solve it using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 2, b = -100, and c = 80000, which we obtained from comparing the equation with the standard quadratic form (ax^2 + bx + c = 0).
Substituting these values into the quadratic formula:
x = (-(-100) ± √((-100)^2 - 4 * 2 * 80000)) / (2 * 2)
Simplifying:
x = (100 ± √(10000 - 640000)) / 4
x = (100 ± √(-630000)) / 4
Since the number inside the square root is negative, it means that there are no real solutions. In this case, it means that the revenue of $800 cannot be achieved by producing and selling this product.