Question

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?

Answer 1

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

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