The total cost of producing a certain good is given by TC=300ln(q+30)+150. Find the marginal cost (MC) and the avarage cost (AC) functions.

To find the total cost of producing 20 units of output given the marginal cost function \( MC = \frac{10}{Q} \) and the total cost is 500 when \( Q = 10 \), follow these steps: 1. **Understand the relationship between total cost and marginal cost**: The total cost \( TC \) can be found by integrating the marginal cost \( MC \) and adding the fixed cost \( C \). 2. **Set up the integral for total cost**: \[ TC(Q) = \int MC \, dQ + C \] Given \( MC = \frac{10}{Q} \), we have: \[ TC(Q) = \int \frac{10}{Q} \, dQ + C \] 3. **Find the antiderivative**: \[ \int \frac{10}{Q} \, dQ = 10 \ln|Q| + C \] So, \[ TC(Q) = 10 \ln|Q| + C \] 4. **Use the given information to find the constant \( C \)**: Given that \( TC(10) = 500 \): \[ 500 = 10 \ln(10) + C \] \[ C = 500 - 10 \ln(10) \] 5. **Find the total cost for \( Q = 20 \)**: \[ TC(20) = 10 \ln(20) + C \] Substitute \( C \): \[ TC(20) = 10 \ln(20) + 500 - 10 \ln(10) \] Simplify: \[ TC(20) = 10 (\ln(20) - \ln(10)) + 500 \] \[ TC(20) = 10 \ln\left(\frac{20}{10}\right) + 500 \] \[ TC(20) = 10 \ln(2) + 500 \] 6. **Calculate the numerical value**: \[ \ln(2) \approx 0.6931 \] \[ TC(20) = 10 \times 0.6931 + 500 \] \[ TC(20) = 6.931 + 500 \] \[ TC(20) \approx 506.93 \] So, the total cost of producing 20 units of output is approximately \( 506.93 \). The correct answer is: - \( 506.93 \)

Tony owns a fancy Italian restaurant, Tony’s Trattoria. He uses only the finest ingredients and hires the best chefs in the country. Suppose Tony’s total cost function is given by the following relationship: TC = 11 + 9Q + 8Q2, where Q is the number of meals prepared in an hour. Calculate Tony’s average total cost (ATC) and marginal cost (MC) as functions of Q. Based on your answer, if Tony wants to minimise his average total cost, how many meals should he produce each hour? Enter the number of meals in the space below.Please round your answer to three decimal places (e.g., write 1/3 as 0.333 and 2/3 as 0.667).

The marginal cost function for producing x units is 3x2 – 200x +1500 rupees. Find the increase in cost if production is increasedfrom 90 to 100 units.

The cost (in dollars) of producing x units of a certain commodity is C(x) = 7000 + 10x + 0.05x2.(a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.)(i)    x = 102$ per unit(ii)    x = 101$ per unit(b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.)

The marginal cost function of manufacturing x units of a product is 5+16x – 3x2 . The total cost of producing 5 items is GHC500. Find the total cost