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

Is the equation 2x2 $$2x^2$$

anonymous · Answer

Yes it is, sorry

anonymous · 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
$$B(x)=x^2−30x+520$$

anonymous · Answer

Are you in a hurry & need the question?

anonymous · Answer

Oh that helps a lot. Could I just use a graphing calculator to graph the functions and compare their minimums?
And yes

anonymous · 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.

anonymous · Answer

In other words the last answer is the right one.

anonymous · Answer

Okay thank you very much!

anonymous · Answer

Your welcome.