The revenue achieved by selling x graphing calculators is figured to be x(45 - 0.5x) dollars.
The cost of each calculator is $25. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $3030.00?
R = 45 x - .5 x^2
C = 25 x
3030 = 20 x - .5 x^2
.5 x^2 - 20 x + 3030 = 0
This has only complex roots. I suspect a typo.
To find the number of graphing calculators that must be sold to make a profit of at least $3030.00, we need to set up an equation and solve for the value of 'x'.
The equation for revenue is given as x(45 - 0.5x) dollars. The cost of each calculator is $25. So, the profit from selling 'x' calculators can be calculated as (x(45 - 0.5x)) - (25x) dollars.
We want this profit to be at least $3030.00. Therefore, we can set up the following equation:
(x(45 - 0.5x)) - (25x) ≥ 3030
First, let's simplify this equation:
45x - 0.5x^2 - 25x ≥ 3030
Combining like terms:
20x - 0.5x^2 ≥ 3030
Now, rearrange the equation to bring all terms to one side:
0.5x^2 - 20x + 3030 ≤ 0
To solve this quadratic inequality, we need to factor it or use the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For our quadratic inequality, the coefficients are:
a = 0.5
b = -20
c = 3030
Substituting these values into the quadratic formula:
x = (-(-20) ± √((-20)^2 - 4(0.5)(3030))) / (2 * 0.5)
Simplifying further:
x = (20 ± √(400 - 6060)) / 1
x = (20 ± √(-5660)) / 1
Since the value inside the square root is negative, it means that there are no real solutions to the equation. In other words, it is not possible to sell a positive number of calculators to achieve a profit of at least $3030.00.
Hence, it is not possible to achieve a profit of at least $3030.00 by selling graphing calculators in this scenario.