Final answer:
The quadratic equation C(x) = 187.5x² - 1500x + 4000 has no real solutions.
Step-by-step explanation:
This expression is a quadratic equation of the form ax² + bx + c = 0, where the constants a = 187.5, b = -1500, and c = 4000. To find the solutions of the equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula, we get:
x = (-(-1500) ± √((-1500)² - 4 * 187.5 * 4000)) / (2 * 187.5)
This can be simplified to:
x = (1500 ± √(2250000 - 3000000)) / 375
The expression inside the square root simplifies to -750000, which is negative. Therefore, the quadratic equation C(x) = 187.5x² - 1500x + 4000 has no real solutions.