Question

E Cost (In Dollars) Of Producing Q Items Is Given By C(Q)=0.01q³−0.6q²+13q

A. Find The Marginal Cost Function.
B. Find The average cost function.
C. Find the production level that will minimize average cost.
D. What is the minimum average cost?

Answer 1

The marginal cost function is MC(Q) = 0.03Q² - 1.2Q + 13. The average cost function is AC(Q) = 0.01Q² - 0.6Q + 13. The production level that will minimize average cost is Q = 30 and the minimum average cost is 10.7 dollars.

Step-by-step explanation:

A. The marginal cost function is the derivative of the cost function. Taking the derivative of C(Q) = 0.01Q³ - 0.6Q² + 13Q, we get MC(Q) = 0.03Q² - 1.2Q + 13.

B. The average cost function is the total cost divided by the quantity. So AC(Q) = C(Q)/Q = (0.01Q³ - 0.6Q² + 13Q)/Q = 0.01Q² - 0.6Q + 13.

C. To find the production level that will minimize average cost, we can take the derivative of AC(Q) and set it equal to 0. Solving the equation 0.02Q - 0.6 = 0, we get Q = 30.

D. The minimum average cost can be found by plugging the value of Q = 30 into the average cost function AC(Q) = 0.01Q² - 0.6Q + 13. So the minimum average cost is AC(30) = 10.7 dollars.