Question

For the given cost function C(x)=52900+300x+x², First, find the average cost function. Use it to find: a) The production level that will minimize the average cost x= b) The minimal average cost

Answer 1

To find the average cost function, divide the total cost by the number of units produced. To find the production level that minimizes the average cost, find the derivative of the average cost function and set it equal to zero. To find the minimal average cost, substitute the value of x that minimizes the average cost into the average cost function.

Step-by-step explanation:

To find the average cost function, we divide the total cost by the number of units produced. In this case, the cost function is C(x)=52900+300x+x². To find the average cost function, we divide this function by x, the number of units produced. So, the average cost function is AC(x) = (52900+300x+x²)/x.

To find the production level that will minimize the average cost, we need to find the derivative of the average cost function and set it equal to zero. Then solve for x. To find the minimal average cost, we substitute the value of x that minimizes the average cost into the average cost function.