Question
A manufacturer keeps track of her monthly costs by using a cost function that assigns total cost for a given number of manufactured items,x. The function is given by C(x)=5,000+1.3x.

A. Can any value be in the domain for this function? What is the domain?

B. If costs must be kept below 10,000 this months, what is the greatest number of items she can manufacture?

A)

No,  you can't make a negative number of items or a fraction.  The domain is positive integers , 1,2 , 3 ....

B)

You want C(x) = 5,000 + 1.3x < 10,000

1.3x < 5,000

x < 5,000/1.3

x < 3846.15

x must be the biggest whole number less than 3846.15 , so x is 3846.

The largest number of items that can be manufactured is 3846
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Volunteer

#### Socrates

##### Expertise

I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.

##### Experience

Ph.D. in Mathematics and many years teaching undergraduate courses at three state universities.

Education/Credentials
B.S. , M.S. , Ph.D.