Question

A company's marginal cost function is given by MC(x)= x + 30 Find the total cost for making the first 10 units. Do not include units

Answer 1

The total cost for making the first 10 units is found by integrating the marginal cost function MC(x) = x + 30 from 1 to 10, yielding a result of 350.

Step-by-step explanation:

To calculate the total cost for making the first 10 units when given a marginal cost function MC(x) = x + 30, we need to integrate the marginal cost function from the first unit to the tenth unit. The marginal cost function represents the additional cost of producing one more unit of a good or service.

Step-by-step Calculation

1. The marginal cost function MC(x) is x + 30.

2. To find total cost (TC), integrate the MC function with respect to x from 1 to 10.

3. The integration of MC(x) = x + 30 is 0.5*x^2 + 30x + C, where C is the constant of integration which represents the fixed cost (Total Cost when x = 0).

4. Assuming the fixed cost C = 0 for simplicity, plug in the upper limit of the integral (x = 10) and subtract the value when x = 0.

5. Total Cost for 10 units, TC(10) = 0.5*10^2 + 30*10 = 50 + 300 = 350.

Therefore, the total cost for making the first 10 units is 350.