Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.001x° + 0.07x² + 16x + 700, and currently 50 chairs are produced monthly. a)What is the current monthly cost? b)What would be the additional cost of increasing production to 51 chairs monthly? c)What is the marginal cost when x= 50? d)Use the marginal cost to estimate the difference in cost between producing 50 and 52 chairs per month. e)Use the answer from part (d) to predict C(52). a) The current monthly cost is $ (Round to the nearest cent as needed.)
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A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
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part a b c d e
![### Monthly Cost Analysis of Chair Production
#### Problem Statement
Suppose that the monthly cost, in dollars, of producing \( x \) chairs is given by the function:
\[ C(x) = 0.001x^3 + 0.07x^2 + 16x + 700 \]
It is known that currently 50 chairs are being produced monthly.
#### Questions and Solutions
a) **What is the current monthly cost?**
- Calculate \( C(50) \).
b) **What would be the additional cost of increasing production to 51 chairs monthly?**
- Find \( C(51) - C(50) \).
c) **What is the marginal cost when \( x = 50 \)?**
- Calculate \( C'(x) \) and evaluate it at \( x = 50 \).
- The polynomial \( C(x) \) should be differentiated to find the marginal cost function \( C'(x) \).
d) **Use the marginal cost to estimate the difference in cost between producing 50 and 52 chairs per month.**
- Utilize \( C'(50) \) to estimate \( C(52) - C(50) \).
e) **Use the answer from part (d) to predict \( C(52) \).**
- Using the result of part (a), add the marginal cost estimations to find \( C(52) \).
#### Steps
a) The current monthly cost is $ ___.
- (Round to the nearest cent as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F039749f4-f96d-4ee7-b1ec-44c2ffd9e17b%2Ffdf8e268-0237-40f3-b91a-979d9329e986%2Fn15cay.png&w=3840&q=75)
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