kara's custom tees experienced fixed costs of $200 dollars and variable costs of $3 dollars a shirt

Question

thereisnousername · Answer

whats the question

erniellyd28 · Answer

im having trouble as how to get to the answer

thereisnousername · Answer

well I need to know what the question is in order to help

erniellyd28 · Answer

write an equation that can be used to determine the total expenses encountered by karas custom tees

calculusxy · Answer

I approach it in with this thinking:

$-$The fixed cost is always there (aka the y-intercept), which in this case is $200. 
$-$The variable cost is the one that is there "per" shirt, or it's $3. Since we don't really know the number of shirts there are, we can leave it as $x$. Also note that this represents the $\text{slope}$ too. 

IN the case of writing it as a slope-intercept form, we can have it as: $y = $200 + $3x$.

erniellyd28 · Answer

so c(x) is 200?

erniellyd28 · Answer

and the cost is $3?

calculusxy · Answer

Not really. We can't determine $c(x)$ accurately because we are not given direct numbers. We are to only write an equation that can be used when we know the number of shirts are being said to us. 

We know that $200 is the fixed price. It will not budge at all. Therefore, it stays in the equation as a constant. We also know that the variable cost is $3, which is there PER shirt. Since we don't know the # of shirts, we can leave it as a variable $x$. 

Therefore, the equation that we can write is: $c(x) = $3x + $200$.

erniellyd28 · Answer

let x be the number of shirts, and let c(x) be the total cost of producing x shirts.

the cost of producing 8 shirts is $?

calculusxy · Answer

Is this related to the question you originally posted?

erniellyd28 · Answer

yes maam

erniellyd28 · Answer

im very sorry

erniellyd28 · Answer

im not trying to make your job harder

calculusxy · Answer

So replace x with 8 because now we know what the # of shirts is. 

$$\large c(8) = $200 + $3(8)$$
Evaluate that to get the answer.

erniellyd28 · Answer

224?

calculusxy · Answer

Correct!

erniellyd28 · Answer

so the cost of producing 8 shirts is 224?

erniellyd28 · Answer

and what do i put for c(x)?

erniellyd28 · Answer

8?

calculusxy · Answer

x = 8. 
So you would have to say c(8) = $224

erniellyd28 · Answer

thank you very much for your help and im sorry for the not including the other details

calculusxy · Answer

You're welcome and no worries :)

erniellyd28 · Answer

have a good night :-)