Question

Let x give the number of gizmos produced in a factory. The total cost in dollars is given by the function C(x) = 9000 + 68x + 0.009x³. Complete the following sentences. Round each answer to two decimal places.

a. The fixed cost is $9000.
b. The variable cost is 68x.
c. The total cost increases as x increases.
d. The total cost is a polynomial function of degree 3.

Answer 1

The cost function given is C(x) = 9000 + 68x + 0.009x³ where $9000 is the fixed cost, 68x + 0.009x³ represents the variable cost, and the total cost is a cubic polynomial function of the quantity produced.

Step-by-step explanation:

The question involves understanding the cost function of producing gizmos in a factory. The fixed cost is clearly identified in the function as the constant term, which is $9000. This is the cost incurred by the factory even when no gizmos are produced. As production levels (x) increase, the variable cost (which is 68x in this case) is added to the fixed cost. In addition to this, there's a cubic term (0.009x³) which also contributes to the variable cost, but with a non-linear relationship to the production levels.

Complete sentences based on the given function would be:

• 
  
• The fixed cost is $9000.
• 
  
• The variable cost can be represented as 68x + 0.009x³.
• 
  
• The total cost increases as the number of gizmos produced (x) increases.
• 
  
• The total cost function C(x) = 9000 + 68x + 0.009x³ is a polynomial function of degree 3, reflecting the level of complexity in the relationship between the number of units produced and the total cost.