The total cost of producing x units of a certain commodity is C(x) thousand dollars, where $C(x)=x^{3}-20 x^{2}+179 x+242.$ a. Find A'(x), where $A(x)=\frac{C(x)}{x}$ is the average cost function. b. For what values of x is A(x) increasing? For what values is it decreasing? c. For what level of production x is average cost minimized? What is the minimum average cost?

Let $p=(10-3 x)^{2}$ for $0 \leq x \leq 3$ be the price at which x hundred units of a certain commodity will be sold, and let R(x) = xp(x) be the revenue obtained from the sale of the x units. Find the marginal revenue R'(x), and sketch the revenue and marginal revenue curves on the same graph. For what level of production is revenue maximized?

If C(x) = 16000 + 200x + 4x^3/2, in dollars, find (i) the cost, average cost, and marginal cost at a production level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost.

Let the total cost of producing x units, c(x), be given by c(x) = kx1−b (0<b<1). This cost curve is called the learning or experience cost curve. a. Show that the cost of producing a unit is a decreasing function of the number of units that have been produced. b. Suppose that each time the number of units produced is doubled, the per-unit product cost drops to r% of its previous value (because workers learn how to perform their jobs better). Show that r = 100(2−b).

The cost C(x) of producing x units of a particular commodity is given. (a) Find the marginal cost C'(x). (b) Determine the level of production x for which the average cost $A(x)=\frac{C(x)}{x}$ is minimized. $C(x)=12 \sqrt{x} e^{x / 10}$

The cost, in dollars, of producing x units of a certain commodity is

$$C(x)=920+2x-0.02x^2+0.00007x^3$$

Find the marginal cost function.

Why are eddy current losses important design factors in ferromagnetic materials but less important in ferrimagnetic materials?

Consider the function

$$g(x)=\left\{\begin{array}{ll}{2 x+1} & {\text { if } x<-1} \\ {x-4} & {\text { if } x \geq-1}\end{array}\right.$$

Find g(2).

Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points. $F(x)=(x-4)^{7 / 3}$

Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.

$$F(x)=(x-4)^{7 / 3}$$

Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.

$$f(x)=x(2 x+1)^2$$

Suppose the total cost of producing x units of a particular commodity is modeled by

$$C(x)=\frac{1}{7} x^{2}+4 x+100$$

and that each unit of the commodity can be sold for

$$p(x)=\frac{1}{4}(80-x)$$

dollars. (a.) What is the marginal cost? (b.) What is the price when the marginal cost is 10? (c.) Estimate the cost of producing the 11 unit. (d.) Find the actual cost of producing the 11 unit.

The cost of producing x units of a product is modeled by C=100+25x-120 In x, $x \geq 1$. (a) Find the average cost function $\bar{C}$. (b) Find the minimum average cost analytically. Use a graphing utility to confirm your result.

Cost The cost of producing x units of a product is modeled by

$$C=100+25 x-120 \ln x, \quad x \geq 1 .$$

Find the average cost function $\bar{C}$.