Bread-Even Analysis: Solving for t

[duki]

Hey guys, here's the problem and what I've got so far.

A contractor purchases a piece of equipment for $36500 that costs an average of $9.25 per hour for fuel and maintenance. The equipment operator is paid $13.50 per hour, and customers are charged $30 per hour.

(a) Write an equation for the cost C of operating this equipment for t hours
(b) Write an equation for the revenue R derived from t hours of use
(c) Find the break-even point for this equipment by finding the time at which R = C

What I've got:

(a)
$$C = 22.75(t)+36500$$

(b)
$$R=30(t)+36500$$

(c - worked out)
$$0 = -7.25(t) + 36500$$
$$5034.48 = t$$
does this look right?

 

[HallsofIvy]

Hey guys, here's the problem and what I've got so far.

A contractor purchases a piece of equipment for $36500 that costs an average of $9.25 per hour for fuel and maintenance. The equipment operator is paid $13.50 per hour, and customers are charged $30 per hour.

(a) Write an equation for the cost C of operating this equipment for t hours
(b) Write an equation for the revenue R derived from t hours of use
(c) Find the break-even point for this equipment by finding the time at which R = C

What I've got:

(a)
$$C = 22.75(t)+36500$$

Yes, that's good. For a moment I didn't reconize that the "22.75" includes both fuel and maintenance and the operator!

(b)
$$R=30(t)+36500$$

No! The cost of the equipment is not Revenue. R= 30 t. Was that a typo? You don't use it in C.

(c - worked out)
$$0 = -7.25(t) + 36500$$
$$5034.48 = t$$
does this look right?

I would recommend showing a little more work. "Break even" occurs when revenue= cost: 30 t= 22.75 t+ 36500. Subtracting 22.75 t from both sides,
7.25 t= 36500 so t= 36500/7.25= 5034.48.

The break even point will occur after 5034.48 hours of use. The "units", hours, is an important part of the answer: not just "503448"!

Showing, and explaining, every detail, as well as specifically answering the question with a full sentence will shock and amaze your teacher!


(I did wonder what "Bread Even Analysis" was. Determining whether you have enough sandwiches to go around?)

 

[duki]

(I did wonder what "Bread Even Analysis" was. Determining whether you have enough sandwiches to go around?)

ha! I tried to fix it but couldn't

R= 30 t. Was that a typo? You don't use it in C.

So the answer should have been $$R=30t$$ instead? Or did I miss something you said..


On the last part, I did get the right answer but I just need to show more work, correct?

 

[HallsofIvy]

So the answer should have been $$R=30t$$ instead? Or did I miss something you said..

Yes, that was what I said.

On the last part, I did get the right answer but I just need to show more work, correct?

Yes. Of course, your teacher might not require that, but it is always good practice- if nothing else, it helps you organize your thoughts.