Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Suppose the cost of producing $x$ items is given by the equation $C(x)=x^{2}-3 x+2300,$ where $x$ represents the number of items in hundreds, and $C$ the cost in dollars. Determine (a) the overhead cost, (b) the cost of producing 100 items, (c) the cost of producing the 100 th item (the marginal cost at $x=100$ ), (d) the average cost function, (e) the average cost of producing 100 items, (f) the level of production which minimizes the cost and the minimum cost.

(a) 2300(b) 12,000(c) 196(d) $\bar{c}(x)=x-3+2300 / x$(e) 120(f) 1.5,2297.75

Algebra

Chapter 1

Functions and their Applications

Section 6

Economic Functions

Functions

Oregon State University

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

03:18

01:12

Suppose the cost, in dolla…

05:12

(a) If $C(x)$ is the cost …

03:11

If $C(x)$ is the cost of p…

0:00

(a) If $ C(x) $ is the cos…

08:59

$\begin{array}{l}{\text { …

01:01

The total cost of producin…

So for the given problem we want to suppose that the cost of producing items is given by the cost equation C f x equals x squared minus three acts Plus 23:00 approx equations X represents the number of items and hundreds. C. Is the cost in dollars. So we want to determine the overhead cost and the cost of producing 100 items. So the overhead cost is clearly can be 2300 because that's the fixed cost. And then the cost of producing 100 items Is going to be c. 100. Okay. Which is gonna be $12,000. Um And then um since its number of items and hundreds though this would just be one. So it's gonna actually be a little less than that. And then we want to know the cost of producing the 100th item in terms of marginal cost and that we would find marginal costs by taking the derivative of this. So that's how we're going to evaluate it.

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:19

Use the appropriate rules to determine the derivative.$$y=3 x^{2 / 3}-3 …

01:04

The maximum possible demand for a certain commodity is 20,000 tons. The high…

02:17

In 1990 the Massachusetts Non-Resident State Income Tax calls for a tax of $…

01:11

When the price of a certain farm product is 40 cents per bushel, the demand …

02:47

Given $f(x)=|2 x-5|$ (a) At what point is the function not differentiable? (…

05:54

Determine (a) $\lim _{x \rightarrow 3^{+}} \frac{|x-3|}{x-3}\left(\text { b)…

02:21

Find the equations of the lines and plot the lines from Exercise $57$.

01:29

Use the appropriate rules to determine the derivative.$$f(x)=3 x^{3}-7 x…

00:51

Compute the indicated limit.(a) $\lim _{x \rightarrow 0^{+}} \frac{1}{x^…

02:14

Where is the function $f(x)=1 /(x-5)$ discontinuous. Why?