Questions: Find the marginal cost function. C(x)=175+0.3 x The marginal cost function is C'(x)=

Solution Steps

The total cost function is given by \(C(x) = 175 + 0.3x\), where:

• \(a = 175\) represents the fixed cost, which does not change with the level of output.
• \(b = 0.3\) represents the variable cost per unit, which changes with the level of output.

This function describes how the total cost changes as the quantity of goods produced, \(x\), changes.

The marginal cost function, \(C'({x_variable_name})\), is found by taking the first derivative of the total cost function with respect to \(x\). Given the total cost function \(C({x_variable_name}) = a + b{x_variable_name}\), the derivative with respect to \(x\) is: \[C'({x_variable_name}) = \frac{d}{d{x_variable_name}}(a + b{x_variable_name}) = b\] This implies that the marginal cost function is constant and equal to \(b\), the coefficient of \(x\) in the total cost function.

It's assumed that the total cost function is linear, implying the variable cost per unit remains constant regardless of the level of production. Additionally, the model assumes that the cost function can be differentiated, indicating that the cost function is continuous and smooth over the range of production levels considered. Finally, it's assumed that the fixed cost \(a\) does not influence the marginal cost, as marginal cost is concerned only with the variable costs associated with producing one more unit.

Final Answer: