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?
1 answer:
Answer:
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
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