math

posted by .

Suppose the total cost function for manufacturing a certain product C(x) is given by the function below, where C (x) is measured in dollars and x represents the number of units produced. Find the level of production that will minimize the average cost. (Round your answer to the nearest whole number.)

C(x)=0.2(0.01x^2+133)

? units

  • math -

    average cost = totalcost/number of units

    a(x) = C(x)/x
    = 0.2(0.01x + 133/x)

    minimum avg cost is where a'(x) = 0
    a'(x) = .02(.01 - 133/x^2)
    x = 10√133 = 115.3, so 115

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    the cost per hour of running an assembly line in a manufacturing plant is a function of the number of items produced per hour. The cost function is C(x) = 0.28x^2 - 0.7x + 1 where C(x) is the cost per hour in thousands of dollars and …
  2. Economics/Math

    Suppose you are the manager of a small chemical company operating in a competitive market. Your cost of production can be expressed as C = 100 + Q2, where Q is the level of output and C is total cost. a. Is this a short-run cost function?
  3. Algebra

    83. Minimizing Marginal Cost The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to increase …
  4. math

    Suppose the total cost function for manufacturing a certain product C(x) is given by the function below, where C (x) is measured in dollars and x represents the number of units produced. Find the level of production that will minimize …
  5. math

    The daily total cost (in dollars) incurred by Trappee and Sons for producing x cases of TexaPep hot sauce is given by the following function. c(x)=0.000002x^3+3x+453 (a) Find the average cost function C. C = ?
  6. Math

    The daily total cost (in dollars) incurred by Trappee and Sons for producing x cases of TexaPep hot sauce is given by the following function. (a) Find the average cost function C. C = ?
  7. math

    The daily total cost (in dollars) incurred by Trappee and Sons for producing x cases of TexaPep hot sauce is given by the following function. c(x)=0.000002x^3+3x+453 (a) Find the average cost function C. C = ?
  8. Pre-Cal

    The total cost (in thousands of dollars) of a machine manufacturing unit is given by the function T(x) = 300 + 5x, where x is the number of machines produced. What is the average cost (in thousands of dollars) of manufacturing 200 …
  9. Economics

    A Cobb-Douglas production function for new company is given by  f(x,y)  50x 2 5 y 3 5 where x represents the units of labor and y represents the units of capital. Suppose units of Labor and capital cost $100 …
  10. MATH

    11.) A company produces a product for which the variable cost is $12.30 per unit and the fixed costs are $98,000. The product sells for $17.98. Let x be the number of units produced and sold. a.) the total cost for a business is th …

More Similar Questions