The cost function for the manufacture of golf balls is given as:
\[ C(x) = 3650 + 0.67x \]
where:
- \( C(x) \) is the total cost,
- \( 3650 \) is the fixed cost (the cost incurred regardless of the number of golf balls produced),
- \( 0.67x \) is the variable cost (the cost that depends on the number produced, with \( 0.67 \) being the cost per additional golf ball).
Now, let's address each part of your question:
a. What is the slope of the graph of the total cost function?
The slope of the total cost function \( C(x) \) is the coefficient of \( x \) in the equation.
From the equation \( C(x) = 3650 + 0.67x \), the slope is 0.67.
b. What is the marginal cost (rate of change of the cost function) for the product?
The marginal cost is the cost of producing one additional unit (in this case, one additional golf ball). It is represented by the derivative of the cost function with respect to \( x \).
Since the cost function is linear (the derivative is constant), the marginal cost is also equal to the slope.
Thus, the marginal cost is also 0.67.
c. What is the cost of each additional ball that is produced in a month?
As already mentioned earlier, the cost of each additional ball that is produced is equal to the marginal cost, which is 0.67.
Summary:
- Slope of the cost function: 0.67
- Marginal cost: 0.67
- Cost of each additional ball produced: 0.67
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