the revenue R from selling x units of a certain product is given by R=x(20-0.2x)
How many units must be sold to produce a revenue of $500?
You will need to solve for x in the following equation:
500 = x(20-0.2x)
factor it out
500 = 20x -0.2x^2
0.2x^2 - 20x + 500 = 0
divide the whole equation by 0.2
x^2 - 100x + 2500 = 0
(x-50)^2
R=50
i got 500=20x-0.2x^2
whats the next step?
=\
To find out how many units must be sold to produce a revenue of $500, we need to solve the equation R = 500, where R is the revenue and x is the number of units sold.
The equation given is R = x(20 - 0.2x). Let's substitute R with 500 in this equation and solve for x:
500 = x(20 - 0.2x)
To solve the equation, we can first distribute x to both terms in parentheses:
500 = 20x - 0.2x^2
Now move all terms to one side of the equation to create a quadratic equation:
0.2x^2 - 20x + 500 = 0
To solve this quadratic equation, we can use either factoring, completing the square, or the quadratic formula. However, in this case, factoring may be difficult, and completing the square can be cumbersome. So, let's use the quadratic formula:
Given a quadratic equation of the form ax^2 + bx + c = 0, the quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/(2a)
For our equation 0.2x^2 - 20x + 500 = 0, the values are:
a = 0.2
b = -20
c = 500
Now we can substitute these values into the quadratic formula:
x = (-(-20) ± √((-20)^2 - 4(0.2)(500))) / (2 * 0.2)
Simplifying further:
x = (20 ± √(400 + 400)) / 0.4
x = (20 ± √(800)) / 0.4
x = (20 ± 28.28) / 0.4
Now we have two possible solutions for x:
x1 = (20 + 28.28) / 0.4
x1 ≈ 120
x2 = (20 - 28.28) / 0.4
x2 ≈ -20.7
Since the number of units sold cannot be negative, we disregard the negative solution. Therefore, the number of units that must be sold to produce a revenue of $500 is approximately 120 units.