The function C (x) = 600x - 0.3x2 represents total costs for a company to produce a product, where C is the total cost in dollars and x is the number of units sold. What number of units would produce a maximum cost? What is the maximum cost?

1000 units produces a maximum cost of $300,000.

Step-by-step explanation:

C (x) = - 0.3x² + 600x

The equation is a downward parabola. Its maximum is at the vertex, which can be found with:

x = - b / (2a)

Here, a = - 0.3 and b = 600.

x = - (600) / (2 * - 0.3)

x = 1000

The maximum cost is:

C (1000) = 300,000

1000 units produces a maximum cost of $300,000.

You can also use calculus to find the maximum.

C (x) = - 0.3x² + 600x

C' (x) = - 0.6x + 600

0 = - 0.6x + 600

x = 1000