Matt sells burgers and sandwiches. The daily cost of making burgers is $520 more than the difference between the square of the number of burgers sold and 30 times the number of burgers sold. The daily cost of making sandwiches is modeled by the following equation:

C(x) = 2x2 - 40x + 300
C(x) is the cost in dollars of selling x sandwiches.

Which statement best compares the minimum daily cost of making burgers and sandwiches?

Question

Matt sells burgers and sandwiches. The daily cost of making burgers is $520 more than the difference between the square of the number of burgers sold and 30 times the number of burgers sold. The daily cost of making sandwiches is modeled by the following equation:

C(x) = 2x2 - 40x + 300
C(x) is the cost in dollars of selling x sandwiches.

Which statement best compares the minimum daily cost of making burgers and sandwiches?

anonymous · Answer

It is greater for sandwiches than burgers because the approximate minimum cost is $250 for burgers and $292 for sandwiches.

It is greater for sandwiches than burgers because the approximate minimum cost is $100 for burgers and $295 for sandwiches.

It is greater for burgers than sandwiches because the approximate minimum cost is $295 for burgers and $100 for sandwiches.

It is greater for burgers than sandwiches because the approximate minimum cost is $292 for burgers and $250 for sandwiches.

anonymous · Answer

I don't know how to do this at all. Can someone please help with this problem ?

anonymous · Answer

Okay give me a minute, @whpalmer4 I don't know how well I can explain without giving the answer, could u help out w/ explanation :D

anonymous · Answer

Thank you

whpalmer4 · Answer

We're given the formula for the cost of selling $x$ sandwiches:
$$C(x) = 2x^2-40x+300$$
We're told the daily cost of making burgers is $520 more than the difference between the square of the number of burgers sold and 30 times the number of burgers sold.

Let's translate the words into an expression:

"$520 more" -> "+520"
"square of the number of burgers sold": x^2
"30 times the number of burgers": 30x
difference: -
so daily cost of making burgers is
$$B(x) = x^2 -30x + 520$$

whpalmer4 · Answer

So now we have two equations to compare.  We want to know the minimum cost for each one.  Given that these formulas depend on the number of burgers or sandwiches made/sold, won't that minimum be when the number made/sold is 0?  Evaluate each of the two equations with $x=0$ to find the minimum costs.  Note that the numbers in the answers may be slightly different (just to make it a bit harder to guess the answers without doing the problem, I suspect).

anonymous · Answer

So, the answer is:
 
It is greater for burgers than sandwiches because the approximate minimum cost is $292 for burgers and $250 for sandwiches

because it is about 1/2 the total when I make x=0 ?

anonymous · Answer

I'm very confused.

whpalmer4 · Answer

The cost of making 0 sandwiches is$$C(0) = 2(0)^2-40(0)+300 = $$
The cost of making 0 burgers is $$B(0) = (0)^2-30(0)+520 = $$

whpalmer4 · Answer

Are you sure you've copied the problem and answer choices accurately?

anonymous · Answer

so it's 300 and 520 but that is not one of my options

whpalmer4 · Answer

Right, I'm starting to understand your confusion here :-)

anonymous · Answer

Yes, I just checked it again.

whpalmer4 · Answer

The problem is also sloppily written, in my opinion, because it can't make up its mind about whether the formulas describe the cost of making or the cost of selling...

whpalmer4 · Answer

I'd say the last answer choice is the closest one to being correct, although one of the numbers is wrong.

whpalmer4 · Answer

Ask your teacher about it if you get a chance, but I wouldn't lose any sleep over it.  Problem authors make mistakes, too.

anonymous · Answer

Thank you! :)