The profit of an organization is calculated by the function P(x) = x2
– 4000x + 7800000, where x is the number
of units sold. If the net profit is 3800000, find the number of items sold.
Thanks
well, just solve
x^2 - 4000x + 7800000 = 3800000
x^2 - 4000x + 4000000 = 0
(x-2000)^2 = 0
x = 2000
Thanks Steve.
To find the number of items sold, we need to solve the equation P(x) = 3800000, where P(x) is the profit function.
The profit function is given by:
P(x) = x^2 - 4000x + 7800000
Let's set this equation equal to 3800000 and solve for x:
x^2 - 4000x + 7800000 = 3800000
Rearranging the equation:
x^2 - 4000x + 7800000 - 3800000 = 0
x^2 - 4000x + 4000000 = 0
Now we have a quadratic equation in the form of ax^2 + bx + c = 0, where:
a = 1
b = -4000
c = 4000000
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values into the formula:
x = (-(-4000) ± √((-4000)^2 - 4(1)(4000000))) / (2(1))
Simplifying:
x = (4000 ± √(16000000 - 16000000)) / 2
x = (4000 ± √0) / 2
Since the discriminant (√(b^2 - 4ac)) is zero, we have a single solution:
x = 4000 / 2
x = 2000
Therefore, the number of items sold is 2000 units.